学术报告（丁义明 7.26）

Yiming Ding (dingym@whut.edu.cn) Center for Mathematical Sciences, Wuhan University of Technology
 
Abstract

The classical Poincare-Denjoy theory claimed that the irrational rotation number of a circle orientation-preserving homeomorphism is the complete topological invariant.  The entropy of a Bernoulli shift is also a completed isomorphic invariant for Bernoulli shift. In this talk, we investigate the complete topological invariants for expansive Lorenz maps using renormlization, kneading invariant and uniform linearization.    A Lorenz map on I = [0,1] is an interval map f:I → I such that for some c ∈ (0,1) we have 1) f is strictly increasing on [0, c) and on (c, 1];  and  2) f(c-)=1 and f(c+)=0. If, in addition, any two points can be separated by the action of f, then f is said to be (topologically) expansive.  We shall provide the Factorization Theorem of kneading invariant, simultaneous calculation of linearization parameters, combinatorial distance as well as the complete topological invariants for expansive Lorenz maps. The main theorem claims that if an expansive Lorenz map f can be renormalized m (0 ≤ m ≤ ∞) times, then there is a sequence of m+1 points in parameter space associated to f; Two expansive Lorenz maps are topologically conjugate if and only if they admit the same sequence of points, the cluster of points in the sequence are complete topological invariants for expansive Lorenz maps. This is a joint work with Yun Sun.