Topological dynamics of cosine maps

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.

Topological Dynamics of Exponential Maps on Their Escaping Sets

For the family of exponential maps Eκ(z) = exp(z)+κ, we prove an analog of Böttcher’s theorem by showing that any two exponential maps Eκ1 and Eκ2 are conjugate on suitable subsets of their escaping sets, and this conjugacy is quasiconformal. Furthermore, we prove that any two attracting and parabolic exponential maps are conjugate on their sets of escaping points; in fact, we construct an anal...

Topological Invariants, Mulitvalued Maps and Computer Assisted Proofs in Dynamics

We introduce the concept of inheritable properties of multivalued maps and show how this concept, when combined with interval arithmetic and repre-sentable multivalued approximations, may be used in adapting topological methods to computer assisted proofs in dynamics. As our rst example we propose a simple geometric criterion for chaos. A more sophisticated example is the Conley index theory. W...

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.

Probabilistic Topological Maps