Ergodic dynamical systems over the Cartesian power of the ring of p-adic integers

Abstract

For any 1-lipschitz ergodic map $F:{\mathbb{Z}}_p^k\mapsto {\mathbb{Z}}_p^k,k>1\in \mathbb{N},$ there are 1-lipschitz ergodic map $G:{\mathbb{Z}}_p\mapsto {\mathbb{Z}}_p$ and two bijection $H_k$, $T_{k,P}$ that $$G=H_k\circ T_{k,P}\circ F\circ H_k^{-1}\text{ and }F=H_k^{-1}\circ T_{k,P^{-1}}\circ G\circ H_k.$$

T-Functions of several variables: New Criteria for Transitivity

References in corpus (2)

• p-Adic Mathematical Physics
• T-functions revisited: New criteria for bijectivity/transitivity