ERGODICITY CRITERIA FOR NON-EXPANDING TRANSFORMATIONS OF 2-ADIC SPHERES

作者：Anashin Vladimir^*; Khrennikov Andrei; Yurova Ekaterina

来源：Discrete and Continuous Dynamical Systems, 2014, 34(2): 367-377.

DOI：10.3934/dcds.2014.34.367

• Ergodic theory
• 1-Lipschitz dynamics
• 2-adic sphere
• p-adic analysis

In the paper, we obtain necessary and sufficient conditions for ergodicity (with respect to the normalized Haar measure) of discrete dynamical systems < f; S2-r (a)> on 2-adic spheres S2-r (a) of radius 2(-r), r >= 1, centered at some point a from the ultrametric space of 2-adic integers Z(2). The map f: Z(2) -> Z(2) is assumed to be non-expanding and measure-preserving; that is, f satisfies a Lipschitz condition with a constant 1 with respect to the 2-adic metric, and f preserves a natural probability measure on Z(2), the Haar measure mu(2) on Z(2) which is normalized so that mu(2)(Z(2)) = 1.

• 出版日期2014-2