Dynamics of surface diffeomorphisms relative to homoclinic and heteroclinic orbits

DOI10.1080/14689360310001623421zbMath1042.37030arXivmath/0210061OpenAlexW2034127075MaRDI QIDQ4470306

Peter J. Collins

Publication date: 22 June 2004

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0210061

zbMATH Keywords

symbolic dynamicsMarkov partitionsgraph representativetrellisesdynamics for diffeomorphisms in two dimensionsglobal shadowing

Mathematics Subject Classification ID

Approximate trajectories (pseudotrajectories, shadowing, etc.) in smooth dynamics (37C50) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Symbolic dynamics (37B10) Combinatorial dynamics (types of periodic orbits) (37E15) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (12)

UNIVERSAL TRELLISES ⋮ Using periodic orbits to compute chaotic transport rates between resonance zones ⋮ Partitioning two-dimensional mixed phase spaces ⋮ Using heteroclinic orbits to quantify topological entropy in fluid flows ⋮ Markov shifts and topological entropy of families of homoclinic tangles ⋮ Entropy-minimizing models of surface diffeomorphisms relative to homoclinic and heteroclinic orbits ⋮ Using Invariant Manifolds to Construct Symbolic Dynamics for Three-Dimensional Volume-Preserving Maps ⋮ The topology of nested homoclinic and heteroclinic tangles ⋮ Sofic Shifts via Conley Index Theory: Computing Lower Bounds on Recurrent Dynamics for Maps ⋮ Topological dynamics of volume-preserving maps without an equatorial heteroclinic curve ⋮ Graph duality in surface dynamics ⋮ Minimal topological chaos coexisting with a finite set of homoclinic and periodic orbits

Cites Work

• Unnamed Item
• Train tracks and automorphisms of free groups
• Rotation sets and monotone periodic orbits for annulus homeomorphisms
• Growing 1D and quasi-2D unstable manifolds of maps
• A fixed-point theorem for planar homeomorphisms
• Abundance of strange attractors
• Fixed points of surface diffeomorphisms
• Topological methods in surface dynamics
• Train-tracks for surface homeomorphisms
• Homoclinic bifurcations for the Hénon map
• Fixed points of pseudo-Anosov diffeomorphisms of surfaces
• A geometric criterion for positive topological entropy
• On the conjugacy problem for automorphisms of free groups. With an addendum
• Lectures on Nielsen fixed point theory
• Global shadowing of pseudo-Anosov homeomorphisms
• Pruning fronts and the formation of horseshoes
• Symbolic encoding in symplectic maps
• Isotopy Stable Dynamics Relative to Compact Invariant Sets
• Knot-types and bifurcation sequences of homoclinic and transient orbits of a single-degree-of-freedom driven oscillator
• Pseudo-Anosov Maps and Invariant Train Tracks in the Disc: A Finite Algorithm
• Homoclinic tangles-classification and applications
• The Forcing Relation for Horseshoe Braid Types
• Homotopical stability of pseudo-Anosov diffeomorphisms
• Relative periodic point theory

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