A criterion for mixed dynamics in two-dimensional reversible maps

DOI10.1063/5.0040444zbMath1476.37037OpenAlexW3158110920MaRDI QIDQ4989117

Dmitry V. Turaev

Publication date: 20 May 2021

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

Full work available at URL: https://doi.org/10.1063/5.0040444

zbMATH Keywords

homoclinic orbitsnon-conservative dynamics

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Periodic orbits of vector fields and flows (37C27) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Cites Work

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• Attractors and repellers near generic elliptic points of reversible maps
• Invariants of \(\Omega\)-conjugacy of diffeomorphisms with a nongeneric homoclinic trajectory
• Time-reversal symmetry in dynamical systems: a survey
• Reversible systems
• The abundance of wild hyperbolic sets and non-smooth stable sets for diffeomorphisms
• Reversibility vs. synchronization in oscillator lattices
• On three types of dynamics and the notion of attractor
• On the phenomenon of mixed dynamics in Pikovsky-Topaj system of coupled rotators
• Pseudo-normal form near saddle-center or saddle-focus equilibria
• Three types of attractors and mixed dynamics of nonholonomic models of rigid body motion
• Diffeomorphisms with infinitely many sinks
• Maps close to identity and universal maps in the Newhouse domain
• Strange attractors and mixed dynamics in the problem of an unbalanced rubber ball rolling on a plane
• Richness of chaotic dynamics in nonholonomic models of a Celtic stone
• Reversible Mixed Dynamics: A Concept and Examples
• 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
• Merger of a Hénon-like attractor with a Hénon-like repeller in a model of vortex dynamics