Using Invariant Manifolds to Construct Symbolic Dynamics for Three-Dimensional Volume-Preserving Maps

DOI10.1137/16M1086108zbMath1373.37085arXiv1607.07346OpenAlexW2963332421MaRDI QIDQ5739160

Spencer A. Smith, Kevin A. Mitchell, Bryan Maelfeyt

Publication date: 2 June 2017

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.07346

zbMATH Keywords

topological dynamicssymbolic dynamicsinvariant manifoldhomotopy theoryheteroclinic tanglevolume-preserving map

Mathematics Subject Classification ID

Related Items (3)

Melnikov Theory for Two-Dimensional Manifolds in Three-Dimensional Flows ⋮ Computational method for phase space transport with applications to Lobe dynamics and rate of escape ⋮ Topological dynamics of volume-preserving maps without an equatorial heteroclinic curve

Cites Work

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• On the geometry of transport in phase space. I. Transport in k-degree-of- freedom Hamiltonian systems, \(2\leq k<\infty\)
• Transport rates of a class of two-dimensional maps and flows
• The topology of nested homoclinic and heteroclinic tangles
• On the integrability and perturbation of three-dimensional fluid flows with symmetry
• Codimension-one partitioning and phase space transport in multi-degree- of-freedom Hamiltonian systems with non-toroidal invariant manifold intersections
• Topological fluid mechanics of point vortex motions
• Partitioning two-dimensional mixed phase spaces
• Greene's residue criterion for the breakup of invariant tori of volume-preserving maps
• A new topological technique for characterizing homoclinic tangles
• A Study in Three-Dimensional Chaotic Dynamics: Granular Flow and Transport in a Bi-Axial Spherical Tumbler
• The Topology of Chaos
• The chaotic saddle of a three degrees of freedom scattering system reconstructed from cross-section data
• Resonance zones and lobe volumes for exact volume-preserving maps
• Forcing Relations for Homoclinic Orbits of the Smale Horseshoe Map
• Coherent structures and chaotic advection in three dimensions
• Formation of coherent structures by fluid inertia in three-dimensional laminar flows
• Computation of Heteroclinic Arcs with Application to the Volume Preserving Hénon Family
• Trellises Formed by Stable and Unstable Manifolds in the Plane
• Period Three Implies Chaos
• Quadratic volume-preserving maps
• Heteroclinic intersections between invariant circles of volume-preserving maps
• Dynamics of surface diffeomorphisms relative to homoclinic and heteroclinic orbits
• Topological fluid mechanics of stirring
• An Introduction to Fluid Dynamics
• Heteroclinic primary intersections and codimension one Melnikov method for volume-preserving maps
• Finite-time braiding exponents
• Thirty years of turnstiles and transport
• A topological approach to three dimensional laminar mixing
• A numerical and experimental study on advection in three-dimensional Stokes flows
• SYMBOLIC DYNAMICS FROM HOMOCLINIC TANGLES
• Homoclinic tangles-classification and applications
• The chaotic set and the cross section for chaotic scattering in three degrees of freedom
• Topology, braids and mixing in fluids
• Generating topological chaos in lid-driven cavity flow
• Using heteroclinic orbits to quantify topological entropy in fluid flows
• Topological characterization of deterministic chaos: enforcing orientation preservation
• Geometry and topology of escape. II. Homotopic lobe dynamics
• Entropy-minimizing models of surface diffeomorphisms relative to homoclinic and heteroclinic orbits

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