A note on the perturbed monomial mapping
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摘要
In this paper, we present a necessary and suffcient condition that the perturbed monomial mapping is ergodic on a sphere S_(p-1)(1), which is in a combination with Anashin's earlier results about the perturbed monomial ergodic mappings on a sphere S_(p-r)(1), r > 1, completely solve a problem posed by A. Khrennikov about the ergodicity of a perturbed monomial mapping on a sphere.
In this paper, we present a necessary and suffcient condition that the perturbed monomial mapping is ergodic on a sphere S_(p-1)(1), which is in a combination with Anashin's earlier results about the perturbed monomial ergodic mappings on a sphere S_(p-r)(1), r > 1, completely solve a problem posed by A. Khrennikov about the ergodicity of a perturbed monomial mapping on a sphere.
In this paper, we present a necessary and suffcient condition that the perturbed monomial mapping is ergodic on a sphere S_(p-1)(1), which is in a combination with Anashin's earlier results about the perturbed monomial ergodic mappings on a sphere S_(p-r)(1), r > 1, completely solve a problem posed by A. Khrennikov about the ergodicity of a perturbed monomial mapping on a sphere.
引文
[1]S Albeverio,A Yu Khrennikov,P Kloeden.Memory retrieval as a p-adic dynamical system,Biosystems,1999,49:105-115.
[2]V S Anashin.Ergodic transformations in the space of p-adic integers,p-adic mathematical physics,3-24,AIP Conf Proc,826,Amer Inst Phys,Melville,NY,2006.
[3]D L DesJardins,M E Zieve.Polynomial mappings(mod pn),arXiv:math/0103046v1.
[4]H Diao,C E Silva.Digraph representations of rational functions over the p-adic numbers,p-Adic Numbers,Ultrametric Analysis,and Applications,2011,3:23-38.
[5]D Dubischar,V M Gundlach,A Yu Khrennikov,O Steinkamp.Attractors of random dynamical systems over p-adic numbers and a model of noisy cognitive processes,Phys D,1999,130:1-12.
[6]A H Fan,L M Liao.On minimal decomposition of p-adic polynomial dynamical systems,Adv Math,2011,228:2116-2144.
[7]M Gundlach,A Khrennikov,K-O Lindahl.On ergodic behavior of p-adic dynamical systems,Infin Dimens Anal Quantum Probab Relat Top,2001,4:569-577.
[8]M Gundlach,A Khrennikov,K-O Lindahl.Ergodicity on p-adic sphere,In German Open Conference on Probability and Statistics,University of Hamburg,2000:61.
[9]A Khrennikov.Non-Archimedean Analysis:Quantum Paradoxes,Dynamical Systems and Biological Models,Kluwer,1997.
[10]A Yu Khrennikov,K-O Lindahl,M Gundlach.Ergodicity in the p-adic framework,In S Albeverio,N Elander,W N Everitt,and P Kurasov,editors,Operator Methods in Ordinary and Partial Differential Equations(S Kovalevski Symproium,Univ of Stockholm,June 2000),volume 132 of Operator Methods:Advances and Applications,Birkhauser,Basel-Boston-Berlin,2002.
[11]K O Lindahl.On Markovian properties of the dynamics on attractors of random dynamical systems over p-adic numbers,Reports from MASDA,Vaxjo University,June 1999.
[2]V S Anashin.Ergodic transformations in the space of p-adic integers,p-adic mathematical physics,3-24,AIP Conf Proc,826,Amer Inst Phys,Melville,NY,2006.
[3]D L DesJardins,M E Zieve.Polynomial mappings(mod pn),arXiv:math/0103046v1.
[4]H Diao,C E Silva.Digraph representations of rational functions over the p-adic numbers,p-Adic Numbers,Ultrametric Analysis,and Applications,2011,3:23-38.
[5]D Dubischar,V M Gundlach,A Yu Khrennikov,O Steinkamp.Attractors of random dynamical systems over p-adic numbers and a model of noisy cognitive processes,Phys D,1999,130:1-12.
[6]A H Fan,L M Liao.On minimal decomposition of p-adic polynomial dynamical systems,Adv Math,2011,228:2116-2144.
[7]M Gundlach,A Khrennikov,K-O Lindahl.On ergodic behavior of p-adic dynamical systems,Infin Dimens Anal Quantum Probab Relat Top,2001,4:569-577.
[8]M Gundlach,A Khrennikov,K-O Lindahl.Ergodicity on p-adic sphere,In German Open Conference on Probability and Statistics,University of Hamburg,2000:61.
[9]A Khrennikov.Non-Archimedean Analysis:Quantum Paradoxes,Dynamical Systems and Biological Models,Kluwer,1997.
[10]A Yu Khrennikov,K-O Lindahl,M Gundlach.Ergodicity in the p-adic framework,In S Albeverio,N Elander,W N Everitt,and P Kurasov,editors,Operator Methods in Ordinary and Partial Differential Equations(S Kovalevski Symproium,Univ of Stockholm,June 2000),volume 132 of Operator Methods:Advances and Applications,Birkhauser,Basel-Boston-Berlin,2002.
[11]K O Lindahl.On Markovian properties of the dynamics on attractors of random dynamical systems over p-adic numbers,Reports from MASDA,Vaxjo University,June 1999.