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Regular version of the site

Article

О структуре резонансов 1:3 и 1:4 при обратимых возмущениях консервативных кубических отображений Эно

Динамические системы. 2017. Т. 7(35). № 3. С. 229-244.
Самылина Е. А., Шыхмамедов А. И., Казаков А. О.

The paper is devoted to the study of local bifurcations of symmetry breaking which arise under reversible perturbations of conservative reversible systems. We chose a perturbed conservative cubic diffeomorphism of a plane as an example of the model on which such bifurcations were investigated. It is shown that the main symmetry breaking bifurcations here are the so-called reversible pitch-fork bifurcations due to which a symmetric elliptic point becomes a symmetric saddle point and a pair of asymptotically stable and completely unstable points (one point is symmetric to another) appears in its neighborhood. The mechanism of destruction of conservative dynamics is demonstrated on the example of 1:3 and 1:4 resonances, which appear near the elliptic point of conservative cubic
Henon map. In addition, in this paper we present an algorithm for constractig reversible perurbations.
which break down the conservative dynamics in two-dimension maps.