Heterodimensional tangencies on cycles leading to strange attractors

Details Heterodimensional tangencies on cycles leading to strange attractors Heterodimensional tangencies on cycles leading to strange attractors

2008-02-26

arxiv.org/abs/0802.3745v2

Discrete and Continuous Dynamical Systems - Series A (2010) 27-1, 285-300

Mathematics

Dynamical Systems

16 pages, 9 figures. to appear in Discrete Conti. Dynam. Sys

Scientific paper

10.3934/dcds.2010.27.285

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.

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