An example derived from Lorenz attractor

Autor:	Li, Ming, Yang, Fan, Yang, Jiagang, Zheng, Rusong
Rok vydání:	2023
Předmět:	Mathematics - Dynamical Systems 37C10 37C70 37D30 37D45
Druh dokumentu:	Working Paper
Popis:	We consider a DA-type surgery of the famous Lorenz attractor in dimension 4. This kind of surgeries have been firstly used by Smale [S] and Ma\~n\'e [M1] to give important examples in the study of partially hyperbolic systems. Our construction gives the first example of a singular chain recurrence class which is Lyapunov stable, away from homoclinic tangencies and exhibits robustly heterodimensional cycles. Moreover, the chain recurrence class has the following interesting property: there exists robustly a 2-dimensional sectionally expanding subbundle (containing the flow direction) of the tangent bundle such that it is properly included in a subbundle of the finest dominated splitting for the tangent flow. Comment: 26 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2302.02098 Zobrazit plný text záznamu View this record from Arxiv