Knotted periodic orbits in suspensions of Smale's horseshoe: period multiplying and cabled knots

DOI10.1016/0167-2789(86)90076-XzbMath0623.58014OpenAlexW4236057051MaRDI QIDQ1091649

Philip J. Holmes

Publication date: 1986

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(86)90076-x

zbMATH Keywords

horseshoeperiod-doublingHénon mapsknotted periodic orbitsperiod-multiplying bifurcations

Mathematics Subject Classification ID

Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (18)

KNOTTED PERIODIC ORBITS AND CHAOTIC BEHAVIOR OF A CLASS OF THREE-DIMENSIONAL FLOWS ⋮ Undecidability and chaos in word-coded symbolic dynamics ⋮ Computation of Genus and Braid Index for Renormalizable Lorenz Links ⋮ A universality of period doublings -- local crossing number. ⋮ A zeta function for flows with positive templates ⋮ Zeta-functions of renormalizable sub-Lorenz templates ⋮ Quantifying the Role of Folding in Nonautonomous Flows: The Unsteady Double-Gyre ⋮ Exact Torus Knot Periodic Orbits and Homoclinic Orbits in a Class of Three-Dimensional Flows Generated by a Planar Cubic System ⋮ Braid Equivalence in the Hénon Family I ⋮ Forced periodic oscillations and the Jones polynomial ⋮ A universality of period doubling bifurcations ⋮ Topological analysis of chaotic dynamical systems ⋮ Knotted periodic orbits in suspensions of Smale's horseshoe: Extended families and bifurcation sequences ⋮ Quantum Invariants of Templates ⋮ From template analysis to generating partitions. I: Periodic orbits, knots and symbolic encodings ⋮ UNIVERSAL FORM OF RENORMALIZABLE KNOTS IN SYMBOLIC DYNAMICS OF BIMODAL MAPS ⋮ Contact topology and hydrodynamics III: knotted orbits ⋮ Topological analysis of chaotic time series data from the Belousov- Zhabotinskii reaction

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