Strict ergodicity of affine p-adic dynamical systems on Zp
By A. Fan, Mingtian Li, Jia-Yan Yao, Dan Zhou. 2007
57 citations recorded by the source corpus.
Abstract Let p ⩾ 2 be a prime number and let Z p be the ring of all p-adic integers. For all α , β , z ∈ Z p , define T α , β ( z ) = α z + β . It is shown that the dynamical system ( Z p , T α , β ) is minimal if and only if α ∈ 1 + p r p Z p and β is a unit, here r p = 1 (respectively r p = 2 ) if p ⩾ 3 (respectively if p = 2 ), and that when it is minimal, it is strictly ergodic and topologically conjugate to ( Z p , T 1 , 1 ) with an analytic and isometric conjugacy. More importantly, when the system is not minimal, we find all its strictly ergodic components. As application, monomial systems S n , ρ ( z ) = ρ z n on the group 1 + p Z p are also discussed.
Subfields: Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/bb97d2b0bccdaab9b8f67bd57c032cd676e71fd0
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- ON MINIMAL DECOMPOSITION OF p-ADIC POLYNOMIAL DYNAMICAL SYSTEMS (2010, methodology): “Anyway, affine polynomials have been fully studied in [15].”