Heteroclinic primary intersections and codimension one Melnikov method for volume-preserving maps

DOI10.1063/1.166480zbMath0979.37009OpenAlexW2055610195WikidataQ73462839 ScholiaQ73462839MaRDI QIDQ4515135

Héctor E. Lomelí, James D. Meiss

Publication date: 12 November 2000

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/0e702c4debe4fa13300d0dd384fc3ade711f26ae

zbMATH Keywords

volume preserving diffeomorphismshyperbolic fixed points

Mathematics Subject Classification ID

Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Local and nonlocal bifurcation theory for dynamical systems (37G99) Dynamical systems involving smooth mappings and diffeomorphisms (37C05)

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Cites Work

• On integrable mappings of standard type
• Homoclinic bifurcations and the area-conserving Henon mapping
• On the geometry of transport in phase space. I. Transport in k-degree-of- freedom Hamiltonian systems, \(2\leq k<\infty\)
• Resonances in area-preserving maps
• Dynamics of a three-dimensional incompressible flow with stagnation points
• Normal form theory for volume preserving maps
• Quadratic volume preserving maps: An extension of a result of Moser
• On the integrability and perturbation of three-dimensional fluid flows with symmetry
• Transport in 3D volume-preserving flows
• On quadratic symplectic mappings
• Two-dimensional invariant manifolds and global bifurcations: Some approximation and visualization studies
• A discrete-time Garnier system
• Transport through chaos
• Computing the dependence on a parameter of a family of unstable manifolds: generalized Melnikov formulas
• Symplectic maps, variational principles, and transport
• Chaotic transport in the homoclinic and heteroclinic tangle regions of quasiperiodically forced two-dimensional dynamical systems
• Quadratic volume-preserving maps
• Applications of the Melnikov method to twist maps in higher dimensions using the variational approach
• Saddle connections and heteroclinic orbits for standard maps
• Poincaré - Melnikov - Arnold method for analytic planar maps
• Exit times and transport for symplectic twist maps
• Globalizing Two-Dimensional Unstable Manifolds of Maps
• Numerical study of quadratic area-preserving mappings
• A variational principle for invariant odd-dimensional submanifolds of an energy surface for Hamiltonian systems