Gonchenko, MarinaGonchenko, Sergey V.Safonov, Klim A.2023-03-012023-03-012021-041078-0947https://hdl.handle.net/2445/194397For 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.21 p.application/pdfeng(c) American Institute of Mathematical Sciences (AIMS), 2021Teoria de la bifurcacióSistemes dinàmics diferenciablesTeoria ergòdicaSistemes dinàmics de baixa dimensióBifurcation theoryDifferentiable dynamical systemsErgodic theoryLow-dimensional dynamical systemsinfo:eu-repo/semantics/article7309622023-03-01info:eu-repo/semantics/openAccess