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2021-04

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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/194397

Reversible perturbations of conservative Henon-like maps

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https://doi.org/10.3934/dcds.2020343

Abstract

For area-preserving Hénon-like maps and their compositions, we consider smooth perturbations that keep the reversibility of the initial maps but destroy their conservativity. For constructing such perturbations, we use two methods, a new method based on reversible properties of maps written in the so-called cross-form, and the classical Quispel-Roberts method based on a variation of involutions of the initial map. We study symmetry breaking bifurcations of symmetric periodic orbits in reversible families containing quadratic conservative orientable and nonorientable Hénon maps as well as a product of two Hénon maps whose Jacobians are mutually inverse.

Subject

Teoria de la bifurcació, Sistemes dinàmics diferenciables, Teoria ergòdica, Sistemes dinàmics de baixa dimensió

Subject (English)

Bifurcation theory, Differentiable dynamical systems, Ergodic theory, Low-dimensional dynamical systems

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Citation

GONCHENKO, Marina, GONCHENKO, Sergey V. and SAFONOV, Klim A. Reversible perturbations of conservative Henon-like maps. Discrete and Continuous Dynamical Systems-Series A. 2021. Vol. 41, num. 4, pags. 1875-1895. ISSN 1078-0947. [consulted: 11 of August of 2026]. Available at: https://hdl.handle.net/2445/194397

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