Heterodimensional tangencies on cycles leading to strange attractors
classification
🧮 math.DS
keywords
heterodimensionalelementattractorscyclesdiffeomorphismspointssaddlesome
read the original 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.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.