Topological dynamics of two-piece eventually expanding maps

On Eventually Expanding Maps of the Interval

In this paper we conjecture that the piecewise linear map f(x) = px1I[0,1/p)(x)+ (sx − s/p)1I[1/p,1](x), p > 1, 0 < s < 1 which has an expanding, onto branch and a contracting branch is eventually piecewise expanding. We give a partial proof of the conjecture, in particular for values of p and s such that d− ln(p(1−s)+s) ln s e 6 = d− ln p ln s e.

Topological Properties of Linearly Coupled Expanding Maps Lattices

Two{dimensional Topological Dynamics

On topological transitive maps on operator algebras

We consider the transitive linear maps on the operator algebra $B(X)$for a separable Banach space $X$. We show if a bounded linear map is norm transitive on $B(X)$,then it must be hypercyclic with strong operator topology. Also we provide a SOT-transitivelinear map without being hypercyclic in the strong operator topology.

Non-uniformly Expanding Dynamics in Maps with Singularities and Criticalities

We investigate a one-parameter family of interval maps arising in the study of the geometric Lorenz ow for non-classical parameter values. Our conclusion is that for all parameters in a set of positive Lebesgue measure, the map has a positive Lyapunov exponent. Furthermore, this set of parameters has a density point which plays an important dynamic role. The presence of both singular and critic...