Heterodimensional tangencies on cycles leading to strange attractors
Dynamical Systems
2010-07-12 v2
Abstract
In this paper, we study heterodimensional cycles of two-parameter families of 3-dimensional diffeomorphisms some element of which contains nondegenerate heterodimensional tangencies of the stable and unstable manifolds of two saddle points with different indexes, and prove that such diffeomorphisms can be well approximated by another element which has a quadratic homoclinic tangency associated to one of these saddle points. Moreover, it is shown that the tangency unfolds generically with respect to the family. This result together with some theorem in Viana, we detect strange attractors appeared arbitrarily close to the original element with the heterodimensional cycle.
Keywords
Cite
@article{arxiv.0802.3745,
title = {Heterodimensional tangencies on cycles leading to strange attractors},
author = {Shin Kiriki and Yusuke Nishizawa and Teruhiko Soma},
journal= {arXiv preprint arXiv:0802.3745},
year = {2010}
}
Comments
16 pages, 9 figures. to appear in Discrete Conti. Dynam. Sys