2007/03/27 by Yiming Ding, Ding, Yiming · 1 citation
Mathematics · Physics and Astronomy · Computer Science · #Mathematical Dynamics and Fractals #Chaos control and synchronization #Nonlinear Dynamics and Pattern Formation
paper · pdf · doi:10.48550/arxiv.math/0703777
We show that there is a bijection between the renormalizations and proper completely invariant closed sets of expanding Lorenz map, which enable us to distinguish periodic and non-periodic renormalizations. Based on the properties of periodic orbit of minimal period, the minimal completely invariant closed set is constructed. Topological characterizations of the renormalizations and α-limit sets are obtained via consecutive renormalizations. Some properties of periodic renormalizations are collected in Appendix.