Reversible perturbations of conservative Hénon-like maps
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, the original 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 points in reversible families containing quadratic conservative orientable and nonorientable Hénon maps as well as the product of two asymmetric Hénon maps (with the Jacobians $b$ and $b^{-1}$).
math.DS↗