[HG_AP]Non-existence of wandering intervals for asymmetric unimodal maps
ABSTRACT
A natural problem in dynamical systems is the classification of “equivalent” systems. In the real one-dimensional setting, the ordering of the phase space (the circle or a compact interval) gives rise to the question of whether the order of the orbits determines the system. More precisely, one may ask whether two maps that are combinatorially equivalent are topologically conjugate. This problem goes back to Poincaré’s work on circle homeomorphisms, and a positive answer depends on the non-existence of wandering intervals.
In this talk, I will discuss joint work with Professor Weixiao Shen at Fudan University, where we prove that an asymmetric unimodal map (that is, one with different left and right critical orders) has no wandering intervals.
