Attractors and repellers near generic elliptic points of reversible maps

DOI10.1134/S1064562414010207zbMath1301.37013arXiv1212.1931OpenAlexW1985867573MaRDI QIDQ403934

J. Herrera, H. S. Yoon

Publication date: 29 August 2014

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1212.1931

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Boundary value problems for higher-order elliptic equations (35J40)

Related Items (13)

On \(1:3\) resonance under reversible perturbations of conservative cubic Hénon maps ⋮ Dynamics of conservative Bykov cycles: tangencies, generalized Cocoon bifurcations and elliptic solutions ⋮ Mixed dynamics of 2-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies ⋮ On local and global aspects of the 1:4 resonance in the conservative cubic Hénon maps ⋮ On three types of dynamics and the notion of attractor ⋮ Three types of attractors and mixed dynamics of nonholonomic models of rigid body motion ⋮ Antisymmetric diffeomorphisms and bifurcations of a double conservative Hénon map ⋮ On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators ⋮ On mixed dynamics of two-dimensional reversible diffeomorphisms with symmetric non-transversal heteroclinic cycles ⋮ Bifurcations of Cubic Homoclinic Tangencies in Two-dimensional Symplectic Maps ⋮ Reversible perturbations of conservative Hénon-like maps ⋮ Breakdown of symmetry in reversible systems ⋮ A criterion for mixed dynamics in two-dimensional reversible maps

Cites Work

• Universal dynamics in a neighborhood of a generic elliptic periodic point
• Reversible systems
• Persistence of homoclinic tangencies for area-preserving maps
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• On models with non-rough Poincaré homoclinic curves
• Diffeomorphisms with infinitely many sinks
• Newhouse regions for reversible systems with infinitely many stable, unstable and elliptic periodic orbits
• Abundance of attracting, repelling and elliptic periodic orbits in two-dimensional reversible maps
• Homoclinic tangencies of arbitrarily high orders in conservative and dissipative two-dimensional maps
• Homoclinic points near elliptic fixed points
• Homoclinic tangencies of arbitrary order in Newhouse domains.

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