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John Guckenheimer

John Guckenheimer

D-Index & Metrics

Mathematics

D-Index
64
Citations
56085
World Ranking
398
National Ranking
210

Research.com Recognitions

  • 2013 - Fellow of the American Mathematical Society
  • 2013 - Steele Prize for Mathematical Exposition
  • 2009 - SIAM Fellow For contributions to theoretical and computational dynamical systems and mathematical neuroscience.
  • 2008 - Fellow of the American Academy of Arts and Sciences
  • 2001 - Fellow of the American Association for the Advancement of Science (AAAS)
  • 1983 - Fellow of John Simon Guggenheim Memorial Foundation

Overview

John Guckenheimer is affiliated with Cornell University in the United States and specializes in mathematics, focusing primarily on advanced differential equations and dynamical systems. Their research spans several subfields including geometry and topology, nature and landscape conservation, applied mathematics, mathematical physics, and statistics and probability.

Their recent publications cover various aspects of dynamical systems and geometric analysis. Notable papers include:

  • "Mode switching in organisms for solving explore-versus-exploit problems," 2023, published in Nature Machine Intelligence
  • "Dense lines of curvature on convex surfaces," 2020, published in Proceedings of the American Mathematical Society
  • "Continuation methods for principal foliations of embedded surfaces," 2022, published in Journal of Computational Dynamics
  • "Staying the course: iteratively locating equilibria of dynamical systems on Riemannian manifolds defined by point-clouds," 2022, published in Journal of Mathematical Chemistry
  • "Principal Foliations of Surfaces near Ellipsoids," 2021, published in New Zealand Journal of Mathematics

Their frequent coauthors include Debojyoti Biswas, Andrew Lamperski, Yu Yang, Kathleen Hoffman, and Eric S. Fortune.

John Guckenheimer's work has been published in a range of venues such as:

  • Nature Machine Intelligence
  • Journal of Computational Dynamics
  • Journal of Mathematical Chemistry
  • Proceedings of the American Mathematical Society
  • New Zealand Journal of Mathematics

The primary fields of study and topics covered in their research are:

  • Mathematics

  • Geometry and Topology
  • Nature and Landscape Conservation
  • Applied Mathematics
  • Mathematical Physics
  • Statistics and Probability

  • Advanced Differential Equations and Dynamical Systems
  • Geometric Analysis and Curvature Flows
  • Fish biology, ecology, and behavior
  • Mathematical Dynamics and Fractals
  • Markov Chains and Monte Carlo Methods
  • Gaussian Processes and Bayesian Inference
  • Fish Ecology and Management Studies

The scientist has received several honors including:

  • Fellow of the American Mathematical Society, 2013
  • Steele Prize for Mathematical Exposition, 2013
  • SIAM Fellow, 2009, for contributions to theoretical and computational dynamical systems and mathematical neuroscience
  • Fellow of the American Academy of Arts and Sciences, 2008
  • Fellow of the American Association for the Advancement of Science (AAAS), 2001
  • Fellow of John Simon Guggenheim Memorial Foundation, 1983

Best Publications

  • Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields

    John Guckenheimer;Philip Holmes;M. Slemrod

  • The Dynamics of Legged Locomotion: Models, Analyses, and Challenges

    Philip Holmes;Robert J. Full;Dan Koditschek;John Guckenheimer

  • Structural stability of Lorenz attractors

    John Guckenheimer;Robert F. Williams

  • Sensitive dependence to initial conditions for one dimensional maps

    John Guckenheimer

  • Mixed-Mode Oscillations with Multiple Time Scales

    Mathieu Desroches;John Guckenheimer;Bernd Krauskopf;Christian Kuehn

  • The dynamics of density dependent population models.

    J Guckenheimer;G Oster;A Ipaktchi

  • Periodic points and topological entropy of one dimensional maps

    Louis Block;John Guckenheimer;Michal Misiurewicz;Lai Sang Young

  • Isochrons and phaseless sets.

    J. Guckenheimer

  • A SURVEY OF METHODS FOR COMPUTING (UN)STABLE MANIFOLDS OF VECTOR FIELDS

    Bernd Krauskopf;Hinke M. Osinga;Eusebius J. Doedel;Michael E. Henderson

  • Structurally stable heteroclinic cycles

    John Guckenheimer;Philip Holmes

  • Perspectives of Nonlinear Dynamics.

    John M. Guckenheimer;E. Atlee Jackson

  • A Strange, Strange Attractor

    John Guckenheimer

  • Nonlinear oscillations, dynamical systems, and bifurcations of vector fields

    John Guckenheimer;Philip Holmes

  • Three coupled oscillators: mode-locking, global bifurcations and toroidal chaos

    C. Baesens;J. Guckenheimer;S. Kim;R. S. MacKay

  • Fixed point theory of iterative excitation schemes in NMR

    R. Tycko;A. Pines;J. Guckenheimer

  • Kuramoto-Sivashinsky dynamics on the center-unstable manifold

    Dieter Armbruster;John Guckenheimer;Philip Holmes

  • Chaos in the Hodgkin--Huxley Model

    John Guckenheimer;Ricardo A. Oliva

  • Discovering the flight autostabilizer of fruit flies by inducing aerial stumbles

    Leif Ristroph;Attila J. Bergou;Gunnar Ristroph;Katherine Coumes

  • Computing Hopf Bifurcations I

    John Guckenheimer;Mark Myers;Bernd Sturmfels

  • Singular Hopf Bifurcation in Systems with Two Slow Variables

    John Guckenheimer

  • One-Dimensional Dynamics

    John Guckenheimer

Frequent Co-Authors

Philip Holmes
Philip Holmes Princeton University
Ronald M. Harris-Warrick
Ronald M. Harris-Warrick Cornell University
Francisco J. Valero-Cuevas
Francisco J. Valero-Cuevas University of Southern California
Hinke M. Osinga
Hinke M. Osinga University of Auckland
George Oster
George Oster University of California, Berkeley
Axel Timmermann
Axel Timmermann Pusan National University
Bernd Krauskopf
Bernd Krauskopf University of Auckland
Eusebius J. Doedel
Eusebius J. Doedel Concordia University
Henk A. Dijkstra
Henk A. Dijkstra Utrecht University
Shay Gueron
Shay Gueron University of Haifa

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