Bifurcations of three-dimensional diffeomorphisms with non-simple quadratic homoclinic tangencies and generalized Hénon maps |
| |
Authors: | S. V. Gonchenko V. S. Gonchenko J. C. Tatjer |
| |
Affiliation: | (1) Institute for Applied Mathematics and Cybernetics, ul. Uljanova 10, Nizhny Novgorod, 603005, Russia;(2) Departament de Matemàtica Aplicada i Anàlisi, Gran Via de les Corts Catalanes 585, Barcelona, 08007, Spain |
| |
Abstract: | We study bifurcations of periodic orbits in two parameter general unfoldings of a certain type homoclinic tangency (called a generalized homoclinic tangency) to a saddle fixed point. We apply the rescaling technique to first return (Poincaré) maps and show that the rescaled maps can be brought to so-called generalized Hénon maps which have non-degenerate bifurcations of fixed points including those with multipliers e ±iϕ . On the basis of this, we prove the existence of infinite cascades of periodic sinks and periodic stable invariant circles. |
| |
Keywords: | homoclinic tangency rescaling generalized Hénon map bifurcation |
本文献已被 SpringerLink 等数据库收录! |