John Guckenheimer
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American mathematician
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John Guckenheimermathematics Degrees
Mathematics
#1900
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#3017
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#768
USA Rank
Measure Theory
#373
World Rank
#550
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#161
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Mathematics
John Guckenheimer's Degrees
- PhD Mathematics University of California, Berkeley
Why Is John Guckenheimer Influential?
(Suggest an Edit or Addition)According to Wikipedia, John Mark Guckenheimer joined the Department of Mathematics at Cornell University in 1985. He was previously at the University of California, Santa Cruz . He was a Guggenheim fellow in 1984, and was elected president of the Society for Industrial and Applied Mathematics , serving from 1997 to 1998. Guckenheimer received his A.B. in 1966 from Harvard and his Ph.D. in 1970 from Berkeley, where his Ph.D. thesis advisor was Stephen Smale.
John Guckenheimer'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
- Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields (1983) (15178)
- ONE‐DIMENSIONAL DYNAMICS * (1980) (708)
- The Dynamics of Legged Locomotion: Models, Analyses, and Challenges (2006) (703)
- Structural stability of Lorenz attractors (1979) (590)
- Mixed-Mode Oscillations with Multiple Time Scales (2012) (465)
- Sensitive dependence to initial conditions for one dimensional maps (1979) (399)
- The dynamics of density dependent population models (1977) (379)
- Periodic points and topological entropy of one dimensional maps (1980) (335)
- Isochrons and phaseless sets (1975) (327)
- Dynamic model (1989) (267)
- A Survey of Methods for Computing (un)Stable Manifolds of Vector Fields (2005) (265)
- Structurally stable heteroclinic cycles (1988) (248)
- Dynamic Models in Biology (2006) (223)
- Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos (1991) (217)
- A Dynamical Simulation Facility for Hybrid Systems (1993) (210)
- Dopamine modulation of two subthreshold currents produces phase shifts in activity of an identified motoneuron. (1995) (194)
- Discovering the flight autostabilizer of fruit flies by inducing aerial stumbles (2010) (192)
- Dopamine modulation of transient potassium current evokes phase shifts in a central pattern generator network (1995) (178)
- A Strange, Strange Attractor (1976) (170)
- Kuramoto-Sivashinsky dynamics on the center-unstable manifold (1989) (156)
- Bifurcation (2018) (154)
- Activity-independent coregulation of IA and Ih in rhythmically active neurons. (2005) (153)
- Computing Hopf Bifurcations I (1997) (151)
- Fruit flies modulate passive wing pitching to generate in-flight turns. (2009) (147)
- Chaos in the Hodgkin-Huxley Model (2002) (146)
- Fixed point theory of iterative excitation schemes in NMR (1985) (145)
- On a codimension two bifurcation (1981) (141)
- Active and passive stabilization of body pitch in insect flight (2013) (140)
- Singular Hopf Bifurcation in Systems with Two Slow Variables (2008) (139)
- Heteroclinic cycles and modulated traveling waves in systems with O(2) symmetry (1988) (136)
- The invariant constrained equilibrium edge preimage curve method for the dimension reduction of chemical kinetics. (2006) (135)
- An Improved Parameter Estimation Method for Hodgkin-Huxley Models (1999) (133)
- The Forced van der Pol Equation I: The Slow Flow and Its Bifurcations (2003) (133)
- On the bifurcation of maps of the interval (1977) (131)
- Dstool: Computer assisted exploration of dynamical systems (1992) (130)
- Bifurcation of the Hodgkin and Huxley equations: A new twist (1993) (109)
- Planar Hybrid Systems (1994) (103)
- Mapping the dynamics of a bursting neuron. (1993) (98)
- Numerical Computation of Canards (2000) (95)
- Computing Periodic Orbits and their Bifurcations with Automatic Differentiation (2000) (86)
- Bifurcation, Bursting, and Spike Frequency Adaptation (1997) (86)
- Controlling roll perturbations in fruit flies (2015) (85)
- Manipulating the edge of instability. (2007) (85)
- Dimension measurements for geostrophic turbulence (1983) (84)
- Chaotic attractors of relaxation oscillators (2006) (82)
- Dynamics of the Van der Pol equation (1980) (82)
- Estimating the phase of synchronized oscillators. (2008) (81)
- Multiple Bifurcation Problems of Codimension Two (1984) (80)
- A robust hybrid stabilization strategy for equilibria (1995) (79)
- The Forced van der Pol Equation II: Canards in the Reduced System (2003) (78)
- Computing Slow Manifolds of Saddle Type (2012) (76)
- On a four parameter family of planar vector fields (1987) (74)
- A Fast Method for Approximating Invariant Manifolds (2004) (71)
- Convective transitions induced by a varying aspect ratio (1983) (70)
- Random evolutionarily stable strategies. (1978) (70)
- Numerical Analysis of Dynamical Systems (1999) (69)
- Multiple bifurcation problems for chemical reactors (1986) (67)
- Noise in chaotic systems (1982) (66)
- Overexpression of a Hyperpolarization-Activated Cation Current (Ih) Channel Gene Modifies the Firing Activity of Identified Motor Neurons in a Small Neural Network (2003) (64)
- Lateral stability of the spring-mass hopper suggests a two-step control strategy for running. (2009) (63)
- Strange Attractors in Fluids: Another View (1986) (62)
- Paddling mode of forward flight in insects. (2011) (62)
- Homoclinic Orbits of the FitzHugh-Nagumo Equation: Bifurcations in the Full System (2010) (60)
- Shocks and rarefactions in two space dimensions (1975) (57)
- Multiparameter Bifurcation Theory (1986) (57)
- Canards at Folded Nodes (2005) (56)
- Finding the dimension of slow dynamics in a rhythmic system (2012) (56)
- Distortion of S-unimodal maps (1990) (55)
- Chaotic dynamics in systems with square symmetry (1989) (53)
- Return maps of folded nodes and folded saddle-nodes. (2008) (52)
- HOMOCLINIC ORBITS OF THE FITZHUGH-NAGUMO EQUATION: THE SINGULAR-LIMIT (2009) (50)
- Nonlinear convection in a rotating layer: Amplitude expansions and normal forms (1983) (50)
- A Geometric Model for Mixed-Mode Oscillations in a Chemical System (2011) (50)
- Catastrophes and partial differential equations (1973) (49)
- Defining Functions for Multiple Hopf Bifurcations (1997) (47)
- Dissecting the Phase Response of a Model Bursting Neuron (2009) (47)
- The Duck and the Devil: Canards on the Staircase (2001) (45)
- Application of the ICE-PIC method for the dimension reduction of chemical kinetics coupled with transport (2007) (43)
- Dynamical Systems: Some Computational Problems (1993) (41)
- Asymptotic analysis of subcritical Hopf-homoclinic bifurcation (2000) (41)
- Resonance regions for families of torus maps (1989) (40)
- Limit sets ofS-unimodal maps with zero entropy (1987) (40)
- Bifurcations of Relaxation oscillations Near Folded saddles (2005) (37)
- Bifurcations of Dynamical Systems (2010) (36)
- Dopamine modulation of two delayed rectifier potassium currents in a small neural network. (2005) (36)
- Constructing predictive models of human running (2015) (35)
- Symbolic dynamics and relaxation oscillations (1980) (35)
- Unfoldings of Singular Hopf Bifurcation (2011) (32)
- The catastrophe controversy (1978) (32)
- Computing Hopf Bifurcations. II: Three Examples From Neurophysiology (1996) (32)
- Synaptic patterning of left-right alternation in a computational model of the rodent hindlimb central pattern generator (2011) (31)
- A Survey of Methods for Computing (un)stable Manifolds of Vector Fields (2006) (30)
- Review: Roger Temam, Infinite-dimensional dynamical systems in mechanics and physics (1989) (30)
- Estimating Effective Degrees of Freedom in Motor Systems (2008) (30)
- Hartman's theorem for complex flows in the Poincaré domain (1972) (29)
- Parameter estimation for bursting neural models (2008) (29)
- Phase Portraits of Planar Vector Fields: Computer Proofs (1995) (28)
- Control of a spring-mass hopper (2003) (28)
- THE BIFURCATION OF QUADRATIC FUNCTIONS * (1979) (28)
- Towards a Global Theory of Singularly Perturbed Dynamical Systems (1996) (27)
- The dynamics of infant visual foraging. (2004) (27)
- A Dynamical System Toolkit with an Interactive Graphical Interface (1997) (26)
- Invariant manifolds and global bifurcations. (2015) (26)
- Resonant triad interactions in symmetric systems (1992) (26)
- The backward behavior of the Ricci and cross-curvature flows on SL (2,R) (2009) (25)
- Mixed-Mode Oscillations of El Niño–Southern Oscillation (2015) (25)
- Bifurcation Phenomena in Population Models (1976) (24)
- Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems (1989) (24)
- Bifurcation and Catastrophe††AMS (MOS) 1970 SUBJECT CLASSIFICATION: 58F99.‡‡Research supported by National Science Foundation (GP-7952X2) at the Institute for Advanced Study, Princeton, New Jersey. (1973) (24)
- Solving a single conservation law (1975) (22)
- Endomorphisms of the Riemann sphere (1970) (22)
- Bifurcations of relaxation oscillations (2004) (21)
- Absolutely Ω-stable diffeomorphisms (1972) (21)
- Introduction: Differential Equations and Dynamical Systems (1983) (20)
- Axiom ${\text{A + NO}}$ cycles$ \Rightarrow \zeta _f \left( t \right)$ rational (1970) (20)
- Bifurcation and degenerate decomposition in multiple time scale dynamical systems (2002) (19)
- Periodic Orbit Continuation in Multiple Time Scale Systems (2007) (18)
- Caustics and non-degenerate Hamiltonians☆ (1974) (17)
- Bogdanov-Takens bifurcation (2007) (17)
- Reduction of a channel-based model for a stomatogastric ganglion LP neuron (1993) (16)
- Dynamics, Control, and Stabilization of Turning Flight in Fruit Flies (2012) (15)
- Global bifurcations of periodic orbits in the forced Van der Pol equation (2001) (15)
- Dynamical Systems: C.I.M.E. Lectures, Bressanone, Italy, June 1978 (1980) (14)
- From data to dynamical systems (2014) (14)
- Fold-Hopf bifurcation (2007) (14)
- Simple Resonance Regions of Torus Diffeomorphisms (1991) (14)
- Strange attractors in fluid dynamics (1983) (13)
- Simulation for hybrid systems and nonlinear control (1992) (13)
- Dimension estimates for attractors (1984) (13)
- The growth of topological entropy for one dimensional maps (1980) (13)
- Stephen Smale: The Mathematician Who Broke the Dimension Barrier (2000) (13)
- The singular limit of a Hopf bifurcation (2012) (12)
- (Un)predictability of strong El Ni\~no events (2017) (12)
- Shilnikov Homoclinic Bifurcation of Mixed-Mode Oscillations (2014) (12)
- Persistent properties of bifurcations (1983) (11)
- Bautin bifurcation (2007) (11)
- Computer-Generated Proofs of Phase Portraits for Planar Systems (1996) (10)
- Averaging and Perturbation from a Geometric Viewpoint (1983) (10)
- Empirical Modelling of Population Time Series Data: The Case of Age and Density Dependent Vital Rates (2012) (9)
- Computational Environments for Exploring Dynamical Systems (1991) (9)
- One-Parameter Families of Vector Fields on Two-Manifolds: Another Nondensity Theorem (1973) (8)
- Regularity of the singular set of two-dimensional area-minimizing flat chains modulo 3 in R[3] (1973) (8)
- Chapter 8 - Numerical Analysis of Dynamical Systems* (2002) (8)
- Periodic Orbits of Hybrid Systems and Parameter Estimation via AD (2006) (8)
- Rigorous Enclosures of a Slow Manifold (2012) (7)
- Toolkit for nonlinear dynamics (1983) (7)
- Global Analysis of Dynamical Systems Festschrift dedicated to Floris Takens for his 60 th birthday (6)
- Dynamical-systems-theory approach to the wall region (1990) (5)
- Cusp bifurcation (2007) (4)
- Computing Periodic Orbits (2001) (4)
- Locomotion: exploiting noise for state estimation (2018) (4)
- In support of catastrophe theory (1977) (3)
- Using Dynamical System Tools in Matlab (2000) (3)
- Local Codimension Two Bifurcations of Flows (1983) (3)
- Obstacles to Modelling Large Dynamical Systems (1989) (3)
- Torus Maps from Weak Coupling of Strong Resonances (1999) (3)
- Defining Equations for Bifurcations and Singularities (2003) (3)
- Dense lines of curvature on convex surfaces (2020) (2)
- Numerical analysis of bifurcations (2008) (2)
- The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors. By Colin Sparrow (1984) (2)
- Estimating degrees of freedom in motor systems (2006) (2)
- Multiple Time Scale Analysis of a Model Belousov-Zhabotinskii Reaction (2013) (2)
- Complexity of hybrid system models (1997) (2)
- On Computing Connecting Orbits: General Algorithm and Applications to the Sine-Gordon and Hodgkin-Huxley Equations (Special Section on Nonlinear Theory and Its Applications) (1994) (2)
- Hyperbolic Sets, Symbolic Dynamics, and Strange Attractors (1983) (2)
- The forced Van der Pol Equation I : Slow flow and its bifurcation (2003) (2)
- Flight Stability of Mosquitos: A Reduced Model (2014) (2)
- The Birth of Chaos (2013) (2)
- An arresting phenomenon (1987) (2)
- Instabilities and chaos in nonhydrodynamic systems (1985) (2)
- Potassium Currents in a Small Neural Network Dopamine Modulation of Two Delayed Rectifier (2005) (2)
- Clues to Strange Attractors (1985) (2)
- An Introduction to Chaos: Four Examples (1983) (2)
- Stabilization Strategy for Equilibria (1995) (1)
- The cusps of Zeeman's catastrophe machine (1977) (1)
- Fruit flies modulate passive wing pitching to induce in-flight turns (2009) (1)
- Review: Robert L. Devaney, An introduction to chaotic dynamical systems (1987) (1)
- Perspectives of Nonlinear Dynamics, vol. 1. By E. Atlee Jackson (1990) (1)
- Staying the course: iteratively locating equilibria of dynamical systems on Riemannian manifolds defined by point-clouds (2022) (1)
- RIGOROUS ENCLOSURES OF SLOW MANIFOLDS (2012) (1)
- Dynamical Systems Theory for Ecologists: A Brief Overview (1995) (1)
- NEW DIRECTIONS IN DYNAMICAL SYSTEMS: (London Mathematical Society Lecture Note Series 127) (1989) (0)
- Numerical Analysis of Dynamical Systems* *This work was partially supported by grants from the Department of Energy, Air Force Office of Scientific Research and the National Science Foundation. (2002) (0)
- Small, sleek, and in control: The body plan, sensory-neural control, and flight stability of insects (2010) (0)
- Building Dynamic Models (2006) (0)
- 1. What Are Dynamic Models (2006) (0)
- Mathematics & Biology - The Interface: Challenges & Opportunities (1992) (0)
- BIFURCATION OF THE HODGKIN ANDHUXLEY EQUATIONS : A NEW TWISTJ (1995) (0)
- Symbolic Dynamics of Trapezoidal Maps: J.D. Louck and N. Metropolis D. Reidel, Boston, 1986, vii+312pp.,$59.00, £40.25. (1987) (0)
- Roll Control in Fruit Flies (2014) (0)
- DYNAMICAL SYSTEMS AND NUMERICAL ANALYSIS By A. M. STUART and A. R. HUMPHRIES Cambridge University Press, 1996, 709 pp. Price £40.00. ISBN 0 521 49672 1 (1998) (0)
- Rigorous estimation of neuromuscular degrees of freedom requires both fractal dimension and principal component analyses: demonstration using hand motions (2006) (0)
- Singularities in Soap-Bubble-Like and Soap-Film-Like Surfaces (2010) (0)
- The Hopf Bifurcation and Its Applications Section 10 Bifurcation Phenomena in Population Models (0)
- Multiparameter bifurcation theory : proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held July 14-20, 1985, with support from the National Science Foundation (1986) (0)
- ASB/ISB award paper Manipulating the edge of instability (2007) (0)
- Symmetry properties of confined convective states (1992) (0)
- Fruit flies use flight auto-stabilization to recover from aerial ``stumbles'' (2009) (0)
- Periodic Orbits of Vector Fields: Computational Challenges (2000) (0)
- Holomorphic vector fields on CP2 (1971) (0)
- A Smooth Multivariate Interpolation Algorithm (2012) (0)
- Organisms use mode-switching to solve the explore-vs-exploit problem (2023) (0)
- Computation Tools for Analysis of Reduced-Order Models for Aeroengine Instabilities (1999) (0)
- Symmetry Properties of Connned Convective States (2007) (0)
- REPORT The dynamics of infant visual foraging (2004) (0)
- The Role of Geometry in Computational Dynamics (1994) (0)
- Beyond Hyperbolicity: Expansion Properties of One-Dimensional Mappings (1993) (0)
- Simulation and Beyond : Computing in the 21 st Century (2003) (0)
- The interplay of sensorimotor time-delays and noise in multisensory integration* (2006) (0)
- Beyond Simulation — Computing Dynamical Systems (0)
- Computation of eigenvalue resonance in numerical bifurcation problems (1994) (0)
- Locomotion: exploiting noise for state estimation (2018) (0)
- Organisms as Complex Systems By (2011) (0)
- Dynamical Characteristics of Weak Turbulence. (1984) (0)
- Probabilistic Properties of Deterministic Systems (Andrzej Lasota and Michael C. Mackey) (1987) (0)
- Go With the Flow (2005) (0)
- Continuation methods for principal foliations of embedded surfaces (2022) (0)
- Distortion Estimates for Negative Schwarzian Maps. (1988) (0)
- 3. Membrane Channels and Action Potentials (2006) (0)
- Principal Foliations of Surfaces near Ellipsoids (2021) (0)
- Siam past President Lecture (0)
- Computational Tools for Dynamical Systems: An Overview (2008) (0)
- Audio System for Technical Readings All Rights Reserved Audio System for Technical Readings Biographical Sketch List of Tables List of Figures (1994) (0)
- Intrinsic unpredictability of strong El Niño events (2016) (0)
- Structure Control of the Wall Region in a Turbulent Boundary. (1995) (0)
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