The diffusion time of the connecting orbit around rotation number zero for the monotone twist maps
Qiudong Wang
We improve Mather's proof on the existence of the connecting orbit around rotation number zero (Proposition 8.1 in [7]) in this paper. Our new proof not only assures the existences of the connecting orbit, but also gives a quantitative estimation on the diffusion time.
keywords: diffusion time. quantitative stimation Connecting orbit
Periodic attractors versus nonuniform expansion in singular limits of families of rank one maps
William Ott Qiudong Wang
We analyze parametrized families of multimodal $1D$ maps that arise as singular limits of parametrized families of rank one maps. For a generic $1$-parameter family of such maps that contains a Misiurewicz-like map, it has been shown that in a neighborhood of the Misiurewicz-like parameter, a subset of parameters of positive Lebesgue measure exhibits nonuniformly expanding dynamics characterized by the existence of a positive Lyapunov exponent and an absolutely continuous invariant measure. Under a mild combinatoric assumption, we prove that each such parameter is an accumulation point of the set of parameters admitting superstable periodic sinks.
keywords: nonuniformly expanding map admissible family of $1D$ maps parametrized family of maps rank one map absolutely continuous invariant measure. periodic attractor singular limit

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