David Ruelle
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Belgian-French mathematical physicist
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Why Is David Ruelle Influential?
(Suggest an Edit or Addition)According to Wikipedia, David Pierre Ruelle is a Belgian mathematical physicist, naturalized French. He has worked on statistical physics and dynamical systems. With Floris Takens, Ruelle coined the term strange attractor, and developed a new theory of turbulence.
David Ruelle's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Ergodic theory of chaos and strange attractors (1985) (4550)
- Recurrence Plots of Dynamical Systems (1987) (2939)
- On the nature of turbulence (1971) (2637)
- Statistical Mechanics: Rigorous Results (1999) (846)
- Liapunov exponents from time series. (1986) (827)
- Fundamental limitations for estimating dimensions and Lyapunov exponents in dynamical systems (1992) (626)
- A MEASURE ASSOCIATED WITH AXIOM-A ATTRACTORS. (1976) (621)
- Occurrence of strange AxiomA attractors near quasi periodic flows onTm,m≧3 (1978) (596)
- Observables at infinity and states with short range correlations in statistical mechanics (1969) (580)
- The Ergodic Theory of Axiom A Flows. (1975) (478)
- Statistical mechanics of a one-dimensional lattice gas (1968) (472)
- Repellers for real analytic maps (1982) (453)
- The ergodic theory of AxiomA flows (1975) (447)
- Superstable interactions in classical statistical mechanics (1970) (438)
- An inequality for the entropy of differentiable maps (1978) (438)
- Ergodic theory of differentiable dynamical systems (1979) (416)
- Smooth Dynamics and New Theoretical Ideas in Nonequilibrium Statistical Mechanics (1998) (400)
- Zeta-functions for expanding maps and Anosov flows (1976) (383)
- Characteristic Exponents and Invariant Manifolds in Hilbert Space (1982) (354)
- Thermodynamic Formalism: The Mathematical Structures of Classical Equilibrium Statistical Mechanics (1978) (329)
- Chaotic evolution and strange attractors (1989) (329)
- Chance and Chaos (2020) (299)
- Order within chaos : towards a deterministic approach to turbulence (1984) (291)
- Differentiation of SRB States (1997) (285)
- The thermodynamic formalism for expanding maps (1989) (272)
- The Claude Bernard Lecture, 1989 - Deterministic chaos: the science and the fiction (1990) (271)
- Deterministic chaos: the science and the fiction (1995) (268)
- Resonances of chaotic dynamical systems. (1986) (243)
- A mathematical reformulation of Derrida's REM and GREM (1987) (217)
- Positivity of entropy production in nonequilibrium statistical mechanics (1996) (214)
- A review of linear response theory for general differentiable dynamical systems (2009) (213)
- Thermodynamic Formalism: The Mathematical Structure of Equilibrium Statistical Mechanics (2004) (208)
- Currents, flows and diffeomorphisms (1975) (198)
- Occurrence of Strange Axiom A Attractors Near Quasi Periodic Flows on T m , m ≧ 3 (1995) (194)
- Large volume limit of the distribution of characteristic exponents in turbulence (1982) (186)
- A phase transition in a continuous classical system (1971) (179)
- THE STABILITY OF MANY-PARTICLE SYSTEMS (1966) (179)
- Some rigorous results on the Sherrington-Kirkpatrick spin glass model (1987) (177)
- Small random perturbations of dynamical systems and the definition of attractors (1981) (176)
- Natural Nonequilibrium States in Quantum Statistical Mechanics (1999) (171)
- Mean entropy of states in classical statistical mechanics (1967) (164)
- General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium☆ (1998) (161)
- Analycity properties of the characteristic exponents of random matrix products (1979) (158)
- Correlation functions of classical gases (1963) (156)
- Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval (1994) (155)
- An extension of the theory of Fredholm determinants (1990) (151)
- Statistical mechanics on a compact set with $Z^\nu $ action satisfying expansiveness and specification (1972) (148)
- Bifurcations in the presence of a symmetry group (1973) (144)
- SENSITIVE DEPENDENCE ON INITIAL CONDITION AND TURBULENT BEHAVIOR OF DYNAMICAL SYSTEMS (1979) (143)
- A remark on bound states in potential-scattering theory (1969) (135)
- Note concerning our paper: ``On the nature of turbulence'' (1971) (118)
- Extension of the Lee-Yang Circle Theorem (1971) (111)
- Where Can One Hope to Profitably Apply the Ideas of Chaos (1994) (111)
- Probability estimates for continuous spin systems (1976) (104)
- Extending the definition of entropy to nonequilibrium steady states (2003) (99)
- SRB States and Nonequilibrium Statistical Mechanics Close to Equilibrium (1996) (95)
- Renormalization of the Abelian Higgs-Kibble Model (2018) (92)
- Locating resonances for AxiomA dynamical systems (1986) (92)
- Random walk in a random environment and 1f noise (1983) (91)
- A variational formulation of equilibrium statistical mechanics and the Gibbs phase rule (1967) (91)
- Characteristic exponents for a viscous fluid subjected to time dependent forces (1984) (91)
- Entropy Production in Quantum Spin Systems (2000) (90)
- Historical behaviour in smooth dynamical systems (2001) (89)
- Absolutely Singular Dynamical Foliations (2000) (88)
- Applications conservant une mesure absolument continue par rapport àdx sur [0, 1] (1977) (87)
- Cluster Property of the Correlation Functions of Classical Gases (1964) (86)
- MEASURES DESCRIBING A TURBULENT FLOW (1980) (86)
- Chaotic evolution and strange attractors : the statistical analysis of time series for deterministic nonlinear systems (1989) (82)
- Noncommutative algebras for hyperbolic diffeomorphisms (1988) (81)
- States of physical systems (1966) (79)
- Review: R. F. Streater and A. S. Wightman, PCT, Spin and statistics, and all that (1965) (75)
- Equivalence of Gibbs and equilibrium states for homeomorphisms satisfying expansiveness and specification (1992) (74)
- Nonequilibrium statistical mechanics near equilibrium: computing higher-order terms (1998) (74)
- Microscopic fluctuations and turbulence (1979) (73)
- Responses to `Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics', by A. Jaffe and F. Quinn (1994) (73)
- Some remarks on the ground state of infinite systems in statistical mechanics (1969) (73)
- Dynamical Zeta Functions and Transfer Operators (2002) (72)
- Resonances for Axiom ${\bf A}$ flows (1987) (72)
- Strict convexity (“continuity”) of the pressure in lattice systems (1971) (71)
- Differentiation of SRB States: Correction and Complements (2003) (69)
- Rotation numbers for diffeomorphisms and flows (1985) (66)
- Turbulence, strange attractors, and chaos (1995) (65)
- On the use of “small external fields” in the problem of symmetry breakdown in statistical mechanics☆ (1972) (62)
- Dynamical systems with turbulent behavior (1978) (62)
- Generalized zeta-functions for Axiom ${\text{A}}$ basic sets (1976) (60)
- Some remarks on the location of zeroes of the partition function for lattice systems (1973) (60)
- Connection between wightman functions and green functions inp-space (1961) (59)
- Statistical mechanics of vortices in an inviscid two-dimensional fluid (1982) (58)
- Some rigorous results on the Sherrington-Kirkpatrick spin glass model (1987) (58)
- Do turbulent crystals exist (1982) (58)
- One-dimensional Gibbs states and Axiom A diffeomorphisms (1987) (58)
- An extension of the theorem of Milnor and Thurston on the zeta functions of interval maps (1994) (55)
- Is our mathematics natural? The case of equilibrium statistical mechanics (1988) (55)
- Ergodic Theory of Chaos (1985) (55)
- Resonances for intermittent systems (1989) (54)
- Entropy Production in Nonequilibrium Statistical Mechanics (1997) (51)
- The Lorenz attractor and the problem of turbulence (1976) (48)
- On the interpretation of 1/f noise (1983) (48)
- Integral Representations of Invariant States on B* Algebras (1967) (46)
- Conversations on nonequilibrium physics with an extraterrestrial (2004) (46)
- Differentiation of SRB states for hyperbolic flows (2004) (44)
- Responses to: A. Jaffe and F. Quinn, “Theoretical mathematics: toward a cultural synthesis of mathematics and theoretical physics” [Bull. Amer. Math. Soc. (N.S.) 29 (1993), no. 1, 1–13; MR1202292 (94h:00007)] (1994) (43)
- Thermodynamic formalism for maps satisfying positive expan-siveness and speci cation (1992) (43)
- SOME COMMENTS ON CHEMICAL OSCILLATIONS (1973) (40)
- Differentiating the Absolutely Continuous Invariant Measure of an Interval Map f with Respect to f (2004) (40)
- Characterization of Lee-Yang polynomials (2008) (40)
- On Feigenbaum's functional equation g ∘ g(λx) + λg(x) = 0 (1982) (39)
- A theorem on canonical commutation and anticommutation relations (1966) (39)
- Central limit theorems, Lee-Yang zeros, and graph-counting polynomials (2014) (38)
- States of Classical Statistical Mechanics (1967) (37)
- Differentiable dynamical systems and the problem of turbulence (1981) (37)
- Positivity of entropy production in the presence of a random thermostat (1997) (37)
- Diagnosis of dynamical systems with fluctuating parameters (1987) (35)
- Five turbulent problems (1983) (34)
- Chemical Kinetics and Differentiable Dynamical Systems (1981) (34)
- Condensation of lattice gases (1966) (33)
- Integral representation of states on a C∗-algebra (1970) (33)
- What Are the Measure Describing Turbulence (1978) (33)
- CLASSICAL STATISTICAL MECHANICS OF A SYSTEM OF PARTICLES (1963) (32)
- Hydrodynamic turbulence as a problem in nonequilibrium statistical mechanics (2012) (32)
- Thermodynamic Formalism: Contents (2004) (32)
- Structure and f -Dependence of the A.C.I.M. for a Unimodal Map f of Misiurewicz Type (2007) (31)
- Bowen’s Formula for the Hausdorff Dimension of Self-Similar Sets (1983) (30)
- Application of hyperbolic dynamics to physics: Some problems and conjectures (2004) (30)
- Addendum: Ergodic theory of chaos and strange attractors (1985) (29)
- A Mechanical Model for Fourier’s Law of Heat Conduction (2011) (29)
- A Remark on the Equivalence of Isokinetic and Isoenergetic Thermostats in the Thermodynamic Limit (2000) (28)
- A heuristic theory of phase transitions (1977) (27)
- Thermodynamic Formalism: Flows (2004) (27)
- The Mathematician's Brain (2018) (27)
- Location of the Lee-Yang zeros and absence of phase transitions in some Ising spin systems (2012) (24)
- Counting Unbranched Subgraphs (1999) (24)
- From dynamical systems to statistical mechanics and back (1986) (23)
- Statistical mechanics and dynamical systems (1977) (23)
- Zeros of Graph-Counting Polynomials (1999) (22)
- The Mathematician's Brain: A Personal Tour Through the Essentials of Mathematics and Some of the Great Minds Behind Them (2007) (22)
- Analyticity of Green's Functions of Dilute Quantum Gases (1971) (22)
- Sharp determinants (1996) (22)
- Analyticity of the susceptibility function for unimodal Markovian maps of the interval (2005) (21)
- Perturbation theory for Lyapunov exponents of a toral map: Extension of a result of Shub and Wilkinson (2001) (20)
- Spectral properties of a class of operators associated with conformal maps in two dimensions (1992) (20)
- Thermodynamic formalism of maps satisfying positive expansiveness and specification (1992) (20)
- Extremal invariant states (1967) (20)
- Spectral properties of a class of operators associated with maps in one dimension (1991) (19)
- Strange attractors (1980) (17)
- Absence of phase transitions in one-dimensional systems with hard cores (1968) (16)
- How Should One Define Entropy Production for Nonequilibrium Quantum Spin Systems (2001) (16)
- Stable manifolds for maps (1980) (16)
- Analytic completion for dynamical zeta functions (1993) (15)
- Bounds on complexity in reaction-diffusion systems (1986) (15)
- Is there screening in turbulence? (1990) (15)
- Gaps and new ideas in our understanding of nonequilibrium (1999) (15)
- A Property of Zeros of the Partition Function for Ising Spin Systems (1972) (15)
- The Turbulent Fluid as a Dynamical System (1991) (14)
- Ergodic Theory of Axiom a Diffeomorphisms (1975) (14)
- Strange attractors as a mathematical explanation of turbulence (1972) (14)
- Statistical mechanics: A departure from equilibrium (2001) (14)
- On manifolds of phase coexistence (1977) (13)
- Topics in quantum statistical mechanics and operator algebras (2001) (13)
- Zeta Functions and Statistical Mechanics (1975) (13)
- Small random perturbations and the definition of attractors (1983) (12)
- Dynamical zeta functions for maps of the interval (1994) (12)
- Phase Transitions with Four-Spin Interactions (2010) (11)
- Functional equation for dynamical zeta functions of Milnor-Thurston type (1996) (10)
- Linear response theory for diffeomorphisms with tangencies of stable and unstable manifolds—a contribution to the Gallavotti–Cohen chaotic hypothesis (2018) (10)
- Is There a Unified Theory of Nonequilibrium Statistical Mechanics (2003) (10)
- Dynamical Zeta Functions: Where Do They Come from and What Are They Good for ? (1992) (10)
- Some Ill-Formulated Problems on Regular and Messy Behavior in Statistical Mechanics and Smooth Dynamics for Which I Would Like the Advice of Yasha Sinai (2002) (10)
- Singularities of the susceptibility of a Sinai–Ruelle–Bowen measure in the presence of stable–unstable tangencies† (2010) (9)
- Chaotic evolution and strange attractors: Entropy (1989) (9)
- Symmetry breakdown in statistical mechanics (1970) (9)
- STATISTICAL MECHANICS OF QUANTUM SYSTEMS OF PARTICLES (1963) (9)
- Early chaos theory (2014) (8)
- Integral representation of measures associated with a foliation (1978) (8)
- What physical quantities make sense in nonequilibrium statistical mechanics (2008) (8)
- A Generalized Detailed Balance Relation (2015) (7)
- Grace-like polynomials (2000) (7)
- Test of a probabilistic model of evolutionary success (1989) (6)
- Non-Equilibrium Statistical Mechanics of Turbulence (2014) (6)
- Chaos, predictability, and idealization in physics (1997) (6)
- Conceptual problems of weak and strong turbulence (1984) (6)
- A mechanism for speciation based on the theory of phase transitions (1981) (5)
- Varieties of limits to scientific knowledge (1998) (5)
- The obsessions of time (1982) (5)
- The pressure of the geodesic flow on a negatively curved manifold (1981) (5)
- Invariant measures for a diffeomorphism which expands the leaves of a foliation (1978) (5)
- On the nature of turbulence (1971) (5)
- Nonequilibrium Statistical Mechanics and Entropy Production in a Classical Infinite System of Rotators (2006) (5)
- A Theory of Hydrodynamic Turbulence Based on Non-equilibrium Statistical Mechanics (2017) (4)
- Must thermodynamic functions be piecewise analytic? (1981) (4)
- Equilibrium statistical mechanics of one-dimensional classical lattice systems (1975) (4)
- Differentiable Dynamical Systems (1989) (4)
- The origin of life seen from the point of view of non-equilibrium statistical mechanics (2017) (3)
- Biology and nonequilibrium: Remarks on a paper by J.L. England (2015) (3)
- Ergodic Aspects of Turbulence Theory (1985) (3)
- On the asymptotic condition in quantum field theory (2021) (3)
- FIELD THEORY AND STATISTICAL MECHANICS. (1970) (3)
- MEKH-MAT ENTRANCE EXAMINATIONS PROBLEMS (2000) (3)
- SINGULARITIES OF THE SUSCEPTIBILITY OF AN SRB MEASURE IN THE PRESENCE OF STABLE-UNSTABLE TANGENCIES (2010) (3)
- Cracks in the glass menagerie of science (1994) (2)
- Das Erlanger Programm (2010) (2)
- What Are the Measures Describing Turbulence? (Nonlinear Nonequilibrium Statistical Mechanics--Proceedings of the 1978 Oji Seminar at Kyoto,July 10～14,1978) (1979) (2)
- Addendum: ``Some rigorous results on the Sherrington-Kirkpatrick spin glass model'' (1988) (2)
- Hydrodynamic Turbulence as a Nonstandard Transport Phenomenon (2016) (2)
- International Conference on Dynamical Systems in Mathematical Physics, Rennes, 1975, Sept. 14-21 (1976) (2)
- Chaos on demand (1995) (2)
- INTRODUCTION TO THE MODERN THEORY OF DYNAMICAL SYSTEMS By ANATOLE KATOK and BORIS HASSELBLATT. Encyclopedia of Mathematics and its Applications 54, Cambridge University Press, 1995, 822 pp. (1997) (2)
- Here be no dragons (2001) (2)
- [Study of methods of alimentary surveys. Comparison of the value of individual and collective surveys]. (1962) (2)
- Liapunov exponents from time series (1995) (2)
- Chaotic evolution and strange attractors: Axiom A and structural stability (1989) (1)
- From the Theory of Chaos to Nonequilibrium Statistical Mechanics (2012) (1)
- Foreword to the first edition (2004) (1)
- Methodes D'analyse Globale EN Hydrodynamique (1995) (1)
- Is There a Unified Theory of Nonequilibrium Statistical Mechanics? (2003) (1)
- Graph-Counting Polynomials for Oriented Graphs (2018) (1)
- THE PROBLEM OF PHASE TRANSITIONS (1999) (1)
- Two-Dimensional Poiseuille Flow (1985) (1)
- Strange attractors and characteristic exponents of turbulent flows (1980) (1)
- THE STATES OF STATISTICAL MECHANICS (1999) (1)
- Ludwig Boltzmann: The Man Who Trusted Atoms, by Carlo Cercignani (1999) (1)
- Recent results on differentiable dynamical systems (1980) (1)
- 7. A Trip to Nancy with Alexander Grothendieck (2007) (0)
- THERMODYNAMIC BEHAVIOR: ENSEMBLES (1999) (0)
- 19. The Smile of Mona Lisa (2007) (0)
- Chaotic evolution and strange attractors: Extracting geometric information from a times series (1989) (0)
- Chaotic evolution and strange attractors: A bit more on turbulence. The Navier–Stokes equation (1989) (0)
- GROUP INVARIANCE OF PHYSICAL STATES (1999) (0)
- 23. The Beauty of Mathematics (2007) (0)
- Chaotic evolution and strange attractors: Bibliography (1989) (0)
- A Theory of Hydrodynamic Turbulence Based on Non-equilibrium Statistical Mechanics (2017) (0)
- Resonances for intermittent systems (1989) (0)
- Recurrence Plots of Dynamical Systems (1987) (0)
- 20. Tinkering and the Construction of Mathematical Theories (2007) (0)
- A Generalized Detailed Balance Relation (2016) (0)
- Bifurcations in the Presence of a Symmetry (2004) (0)
- Chaotic evolution and strange attractors: Invariant probability measures (1989) (0)
- Identities for Correlation Functions in Classical Statistical Mechanics and the Problem of Crystal States (2020) (0)
- Piecewise monotone maps (2004) (0)
- Chaotic evolution and strange attractors: References (1989) (0)
- THE THERMODYNAMIC LIMIT FOR THERMODYNAMIC FUNCTIONS: LATTICE SYSTEMS (1999) (0)
- Abstracts from the international conference on mathematical problems from the physics of fluids (1986) (0)
- LOW DENSITY EXPANSIONS AND CORRELATION FUNCTIONS (1999) (0)
- THE THERMODYNAMIC LIMIT FOR THERMODYNAMIC FUNCTIONS: CONTINUOUS SYSTEMS (1999) (0)
- Thermodynamic Formalism: Translation invariance. Theory of equilibrium states (2004) (0)
- Can Nonlinear Dynamics Help Economists (2018) (0)
- An inequality for the entropy o f differentiable maps (2007) (0)
- Thermodynamic Formalism: Integral representations on convex compact sets (2004) (0)
- Non-Equilibrium Statistical Mechanics of Turbulence (2014) (0)
- Biology and nonequilibrium: Remarks on a paper by J.L. England (2015) (0)
- Mit Alexander Grothendieck nach Nancy (2010) (0)
- In retrospect chosen by David Ruelle (1998) (0)
- Thermodynamic Formalism: Convexity (2004) (0)
- Two-Dimensional Poiseuille Flow (1985) (0)
- CHAPTER 9 SPECULA TIONS ON FRACTAL GEOMETRY IN SPATIAL DYNAMICS (1993) (0)
- Thermodynamic Formalism: Theory of Gibbs states (2004) (0)
- Is There Screening in Turbulence (1995) (0)
- Ergodic Aspects of Turbulence Theory (1985) (0)
- Identities for Correlation Functions in Classical Statistical Mechanics and the Problem of Crystal States (2020) (0)
- Sharp determinants (1996) (0)
- A Mechanical Model for Fourier’s Law of Heat Conduction (2011) (0)
- General thermodynamic formalism (1975) (0)
- Renormalization of Gauge Theories (2018) (0)
- SHARP DETERMINANTS AND KNEADING OPERATORSFOR HOLOMORPHIC (1995) (0)
- Attracting sets and attractors (1989) (0)
- Thermodynamic Formalism: Statistical mechanics on Smale spaces (2004) (0)
- Wie Mathematiker ticken (2010) (0)
- Thermodynamic Formalism: One-dimensional systems (2004) (0)
- Chaotic evolution and strange attractors: Foreword (1989) (0)
- New methods and problems in statistical mechanics (1970) (0)
- The Hénon mapping (1989) (0)
- Measures and abstract dynamical systems (2004) (0)
- ANNALES DE L'I. H. P., SECTION A (1967) (0)
- Extension of the thermodynamic formalism (2004) (0)
- An introduction to dynamical zeta functions (2004) (0)
- Henri Poincaré's “Science et méthode” (1998) (0)
- Miscellaneous definitions and results (2004) (0)
- 1. Scientific Thinking (2007) (0)
- According to conventional ideas, when the Reynold's number of a fluid is increased a number of independant frequencies, or "asci !lations", successively appear in the fluid. The superposition of a sufficiently large number of frequencies would (1975) (0)
- Thermodynamic Formalism: Gibbs states: complements (2004) (0)
- Chaotic evolution and strange attractors: Capacity and Hausdorff dimension (1989) (0)
- Ergodic Theory of Diffeomorphisms (Symposium on Dynamical Systems) (1978) (0)
- Post-human mathematics (2013) (0)
- Thermodynamic Formalism: Preface to the first edition (2004) (0)
- Graph-Counting Polynomials for Oriented Graphs (2018) (0)
- 4. Mathematics and Ideologies (2007) (0)
- The impact of Thom's cobordism theory (2004) (0)
- Thermodynamic Formalism: Connection between Gibbs states and Equilibrium states (2004) (0)
- Descriptions of turbulence (1989) (0)
- Chaotic evolution and strange attractors: Invariant manifolds (1989) (0)
- The nature of properly human mathematics (2022) (0)
- 16. Mathematical Invention: Psychology and Aesthetics (2007) (0)
- A N EXTENSION OF THE THEORY OF FREDHOLM DETERMINANTS by (2007) (0)
- Fuzzy recurrence plots (2017) (0)
- Thermodynamic Formalism: Update of open problems (2004) (0)
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