Floris Takens | Academic Influence

Floris Takens's AcademicInfluence.com Rankings

Floris Takens

Mathematics

#534

World Rank

#1032

Historical Rank

Measure Theory

#417

World Rank

#603

Historical Rank

mathematics Degrees

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Mathematics

Floris Takens's Degrees

PhD Mathematics University of Amsterdam
Masters Mathematics University of Amsterdam

Why Is Floris Takens Influential?

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According to Wikipedia, Floris Takens was a Dutch mathematician known for contributions to the theory of chaotic dynamical systems. Together with David Ruelle, he predicted that fluid turbulence could develop through a strange attractor, a term they coined, as opposed to the then-prevailing theory of accretion of modes. The prediction was later confirmed by experiment. Takens also established the result now known as the Takens's theorem, which shows how to reconstruct a dynamical system from an observed time-series. He was the first to show how chaotic attractors could be learned by neural networks.

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Floris Takens'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

Detecting strange attractors in turbulence (1981) (9697)
On the nature of turbulence (1971) (2637)
Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations : fractal dimensions and infinitely many attractors (1993) (680)
Occurrence of strange AxiomA attractors near quasi periodic flows onTm,m≧3 (1978) (596)
Measure and category (1988) (572)
Singularities of vector fields (1974) (464)
On the numerical determination of the dimension of an attractor (1985) (433)
Handbook of Dynamical Systems (2010) (382)
Bifurcations and stability of families of diffeomorphisms (1983) (315)
A global version of the inverse problem of the calculus of variations (1979) (230)
Forced oscillations and bifurcations (2001) (216)
Occurrence of Strange Axiom A Attractors Near Quasi Periodic Flows on T m , m ≧ 3 (1995) (194)
Normal forms for certain singularities of vectorfields (1973) (183)
Unfoldings and Bifurcations of Quasi-Periodic Tori (1990) (167)
On the variational principle for the topological entropy of certain non-compact sets (2003) (160)
Constrained equations; a study of implicit differential equations and their discontinuous solutions (1976) (159)
Reversibility as a criterion for discriminating time series (1995) (154)
Unfoldings of certain singularities of vectorfields: Generalized Hopf bifurcations (1973) (141)
Partially hyperbolic fixed points (1971) (127)
HYPERBOLICITY AND THE CREATION OF HOMOCLINIC ORBITS (1987) (121)
Note concerning our paper: ``On the nature of turbulence'' (1971) (118)
Dynamical Systems and Chaos (2010) (104)
Learning Chaotic Attractors by Neural Networks (2000) (98)
The minimal number of critical points of a function on a compact manifold and the Lusternik-Schnirelman category (1968) (89)
Generic properties of geodesic flows (1972) (86)
Heteroclinic attractors: Time averages and moduli of topological conjugacy (1994) (82)
Multifractal Analysis of Local Entropies for Expansive Homeomorphisms with Specification (1999) (81)
Similarity between chaos analysis and frequency analysis of pressure fluctuations in fluidized beds (2004) (78)
DETECTING NONLINEARITIES IN STATIONARY TIME SERIES (1993) (75)
Topological equivalence of normally hyperbolic dynamical systems (1977) (71)
Motion under the influence of a strong constraining force (1980) (69)
Formally symmetric normal forms and genericity (1989) (65)
Cycles and measure of bifurcation sets for two-dimensional diffeomorphisms (1985) (62)
Unfolding and bifurcations of quasi-periodic tori. I: Unfolding of quasi-periodic tori (1990) (62)
Structures in Dynamics: Finite Dimensional Deterministic Studies (1991) (54)
Homoclinic points in conservative systems (1972) (53)
Dynamical systems and bifurcations (1985) (52)
Symmetries, conservation laws and variational principles (1977) (48)
LIMIT CAPACITY AND HAUSDORFF DIMENSION OF DYNAMICALLY DEFINED CANTOR SETS (1988) (42)
An introduction to chaotic dynamical systems (1988) (41)
Implicit differential equations: Some open problems (1976) (40)
Resonances in skew and reducible quasi-periodic Hopf bifurcations (2000) (39)
Intermittency and weak Gibbs states (2000) (38)
GENERALIZED ENTROPIES : RENYI AND CORRELATION INTEGRAL APPROACH (1998) (37)
Stability of parametrized families of gradient vector fields (1983) (37)
Characterization of a differentiable structure by its group of diffeomorphisms (1979) (37)
On Zeeman's tolerance stability conjecture (1971) (34)
Hamiltonian systems: Generic properties of closed orbits and local perturbations (1970) (32)
Some remarks on the Böhme-Berger bifurcation theorem (1972) (32)
A method to estimate the DNA content of whole nuclei from measurements made on thin tissue sections. (1985) (30)
A Nonstabilizable Jet of a Singularity of a Vector Field (1973) (30)
Derivations of vector fields (1973) (27)
Mixed spectra and rotational symmetry (1993) (26)
Spatio-temporal chaos: A solvable model (1997) (26)
Rotation intervals of endomorphisms of the circle (1984) (25)
STABLE ARCS OF DIFFEOMORPHISMS (1976) (21)
A C1 counterexample to Moser's twist theorem (1971) (20)
A note on sufficiency of jets (1971) (20)
Integrable and non-integrable deformations of the skew Hopf bifurcation (1999) (18)
Unicity of KAM tori (2007) (18)
Feasibility of real-time calculation of correlation integral derived statistics applied to EEG time series (2005) (17)
Chapter 7 – Reconstruction Theory and Nonlinear Time Series Analysis (2010) (17)
Multiplications in solenoids as hyperbolic attractors (2005) (15)
The reconstruction theorem for endomorphisms (2002) (14)
Morse Theory of Double Normals of Immersions (1971) (14)
Homoclinic Bifurcations (2010) (13)
Height functions on surfaces with three critical points (1975) (12)
Global properties of integrable Hamiltonian systems (2008) (12)
Neural networks for prediction and control of chaotic fluidized bed hydrodynamics: a first step (1997) (12)
General multifractal analysis of local entropies (2000) (12)
Chapter 3 – Local Invariant Manifolds and Normal Forms (2010) (11)
Estimation of dimension and order of time series (1996) (11)
Constrained Differential Equations (1975) (11)
Preliminaries of Dynamical Systems Theory (2010) (11)
Intermittancy: Global aspects (1988) (9)
Rényi entropies of aperiodic dynamical systems (2002) (9)
Abundance of generic homoclinic tangencies in real-analytic families of diffeomorphisms (1992) (9)
VECTOR FIELDS WITH NO NON-WANDERING POINTS (1976) (7)
Multifractal Analysis of Dimensions and Entropies (2000) (7)
Mechanical and gradient systems; local perturbations and generic properties (1983) (7)
Isolated Critical Points of C∞ and Cω Functions (1967) (7)
Geometry Symposium Utrecht 1980 (1981) (6)
A solution: An exemple as requested in the problem of R. Thom, D 4c (1971) (6)
Moduli and bifurcations; Non-transversal intersections of invariant manifolds of vectorfields (1980) (6)
Robust Learning of Chaotic Attractors (1999) (5)
Dynamical systems and bifurcation theory (1987) (5)
Geometric Aspects of Non-linear R.L.C. Networks (1975) (5)
Chaotic attractor learning and how to deal with nonlinear singularities (2000) (5)
On the nature of turbulence (1971) (5)
The Thermodynamic Formalism (1991) (4)
Homoclinic tangencies: moduli and topology of separatrices (1993) (4)
Reconstruction and time series analysis (2011) (4)
Generic properties of closed geodesics on smooth hypersurfaces (1993) (4)
Reconstruction and Observability, a Survey (1998) (3)
MODULI OF SINGULARITIES OF VECTOR-FIELDS (1984) (3)
NONLINEAR CONTROL SYSTEMS DESIGN 1998, VOLS 1& 2 (1998) (3)
Introduction to global analysis : lectures held at Utrecht State University, October-December 1972 (1973) (2)
Images of SMC Research 1996 (1996) (2)
On Lie algebras of vector fields, Lie algebras of differential operators and nonlinear filtering (1981) (2)
Singularities of Gradient Vector Fields and Moduli (1985) (2)
Global structure of dynamical systems (2011) (2)
Applications of Global analysis : symposium Utrecht State University, February 8, 1973 (1974) (2)
Integral Curves Near Mildly Degenerate Singular Points of Vector Fields (1973) (1)
Examples and definitions of dynamical phenomena (2011) (1)
On symmetric omega-limit sets in reversible flows (1996) (1)
Moduli of Stability for Gradients (1985) (1)
Characterization of compactness for symplectic manifolds (1973) (1)
On the Optimum Finite-Amplitude Motion of a Thrust-Producing Profile (1975) (1)
On Poincaré's geometric investigations of the equations of classical mechanics (1989) (1)
Linear versus nonlinear time series analysis—smoothed correlation integrals (2003) (1)
Examples of manifolds which are homogeneous spaces of lie groups of arbitrarily large dimension (1975) (0)
Qualitative properties and predictability of evolutions (2011) (0)
Applicability and performance of heart rate variability methods (2003) (0)
Multiplications in solenoids as hyperbolic attracto (2005) (0)
PROBLEM SETTING AND SUMMARY OF THE RESULTS We continue the study by Duistermaat (2008) (0)
JÜRGEN MOSER – 80 Global Properties of Integrable Hamiltonian Systems (2008) (0)
Book Review: Introduction to the modern theory of dynamical systems (1996) (0)
EQUADIFF 2003: INTERNATIONAL CONFERENCE ON DIFFERENTIAL EQUATIONS (2005) (0)
Time series analysis : Smoothed correlation integrals, autocovariances, and power spectra (2005) (0)
On KAM theory (2011) (0)
The analysis of correlation integrals in terms of extremal value theory (1998) (0)
Persistence of dynamical properties (2011) (0)
COMPUTERS IN CARDIOLOGY 2003, VOL 30 (2003) (0)
Generalized entropies (1996) (0)
Nonlinear Dynamical Sysems and Chaos, Progress in Nonlinear Differential quations and their Applications (1996) (0)
Mathematical Aspects of Nonlinear Dynamical Systems (1996) (0)
Geometry Symposium, Utlecht 1980 : proceedings of a symposium held at the University of Utrecht, The Netherlands, August 27-29, 1980 (1981) (0)
The Turbulence Paper of D. Ruelle and F. Takens (2001) (0)
Dynamical systems and bifurcations : proceedings of a workshop held in Groningen, the Netherlands, April 16-20, 1984 (1985) (0)
IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. (2017) (0)
1. Context (2012) (0)
Multifractal Analysis of Local Entropies for Gibbs Measures (1998) (0)

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