Entropy-minimizing models of surface diffeomorphisms relative to homoclinic and heteroclinic orbits

DOI10.1080/14689360500133209zbMath1122.37032arXivmath/0311187OpenAlexW1995263809MaRDI QIDQ5711994

Peter J. Collins

Publication date: 22 December 2005

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

Full work available at URL: https://arxiv.org/abs/math/0311187

Mathematics Subject Classification ID

Topological entropy (37B40) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Combinatorial dynamics (types of periodic orbits) (37E15) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (10)

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 ⋮ 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

• Train-tracks for surface homeomorphisms
• Estimation of the number of periodic orbits
• Curves von 2-manifolds and isotopies
• Global shadowing of pseudo-Anosov homeomorphisms
• Dynamics of surface diffeomorphisms relative to homoclinic and heteroclinic orbits
• Homotopical stability of pseudo-Anosov diffeomorphisms
• Relative periodic point theory

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