共查询到20条相似文献,搜索用时 9 毫秒
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Theory of dynamical systems in fields of p-adic numbers is an important part of algebraic and arithmetic dynamics. The study of p-adic dynamical systems is motivated by their applications in various areas of mathematics, physics, genetics, biology, cognitive science, neurophysiology, computer science, cryptology, etc. In particular, p-adic dynamical systems found applications in cryptography, which stimulated the interest to nonsmooth dynamical maps. An important class of (in general) nonsmooth maps is given by 1-Lipschitz functions. In this paper we present a recent summary of results about the class of 1-Lipschitz functions and describe measure-preserving (for the Haar measure on the ring of p-adic integers) and ergodic functions. The main mathematical tool used in this work is the representation of the function by the van der Put series which is actively used in p-adic analysis. The van der Put basis differs fundamentally from previously used ones (for example, the monomial and Mahler basis) which are related to the algebraic structure of p-adic fields. The basic point in the construction of van der Put basis is the continuity of the characteristic function of a p-adic ball. Also we use an algebraic structure (permutations) induced by coordinate functions with partially frozen variables. 相似文献
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E. I. Zelenov 《Theoretical and Mathematical Physics》2014,178(2):194-201
We consider a class of dynamical systems over the p-adic number field: hierarchical dynamical systems. We prove a strong variant of the Poincaré theorem on the number of returns for such systems and show that hierarchical systems do not admit mixing. We describe hierarchical dynamical systems over the projective line and present an example of a nonhierarchical p-adic system that admits mixing: the p-adic baker’s transformation. 相似文献
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We consider p-adic affine dynamical systems on the ring of all p-adic integers, and we find a necessary and sufficient condition for such a system to be minimal. The minimality is equivalent to the transitivity, the ergodicity of the Haar measure, the unique ergodicity, and the strict ergodicity. When the condition is not satisfied, we prove that the system can be decomposed into strict ergodic subsystems. One of our applications is the study of the divisibility, by a power of prime number, of the sequence of integers with positive integers and n. To cite this article: A.-H. Fan et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
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U. A. Rozikov I. A. Sattarov 《P-Adic Numbers, Ultrametric Analysis, and Applications》2014,6(1):54-65
We investigate the behavior of trajectories of a (3, 2)-rational p-adic dynamical system in the complex p-adic field ? p , when there exists a unique fixed point x 0. We study this p-adic dynamical system by dynamics of real radiuses of balls (with the center at the fixed point x 0). We show that there exists a radius r depending on parameters of the rational function such that: when x 0 is an attracting point then the trajectory of an inner point from the ball U r (x 0) goes to x 0 and each sphere with a radius > r (with the center at x 0) is invariant; When x 0 is a repeller point then the trajectory of an inner point from a ball U r (x 0) goes forward to the sphere S r (x 0). Once the trajectory reaches the sphere, in the next step it either goes back to the interior of U r (x 0) or stays in S r (x 0) for some time and then goes back to the interior of the ball. As soon as the trajectory goes outside of U r(x 0) it will stay (for all the rest of time) in the sphere (outside of U r(x 0)) that it reached first. 相似文献
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In the framework of non-Archimedean (p-adic) analysis we study cyclic behaviour of polynomial discrete dynamical systems (iterations of polynomial maps). One of the main tools of our investigation is Hensel's lemma (a p-adic analogue of Newton's method). Our considerations will lead to formulas for the number cycles of a specific length and for the total number of cycles. We will also study the distribution of cycles in the different p-adic fields. 相似文献
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V. Sopin 《P-Adic Numbers, Ultrametric Analysis, and Applications》2014,6(4):333-336
For any 1-lipschitz ergodic map F: ? p k ? ? p k , k >1 ∈ ?, there are 1-lipschitz ergodic map G: ? p ? ? p and two bijections H k , T k, P that $G = H_k \circ T_{k,P} \circ F \circ H_k^{ - 1} andF = H_k^{ - 1} \circ T_{k,P - 1} \circ G \circ H_k $ . 相似文献
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N. I. Chernov 《Functional Analysis and Its Applications》1993,27(1):51-54
United Institute of Nuclear Research. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 27, No. 1, pp. 60–64, January–March, 1993. 相似文献
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C.D Johnson 《Journal of Mathematical Analysis and Applications》1973,44(1):175-186
The classical notion of stabilizing a controlled dynamical system to some specified equilibrium point is extended to include stabilization to a specified linear subspace. Necessary and sufficient conditions for existence of a solution are derived and an explicit solution recipe is given for one special case. 相似文献
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David E. Dobbs 《代数通讯》2013,41(8):3887-3894
We prove that if an extension R ? T of commutative rings satisfies the going-up property (for instance, if T is an integral extension of R), then any increasing chain of prime ideals of R (indexed by an arbitrary linearly ordered set) is covered by some corresponding chain of prime ideals of T. As a corollary, we recover the recent result of Kang and Oh that any such chain of prime ideals of an integral domain D is covered by a corresponding chain in some valuation overring of D. 相似文献
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In this paper, inspired by some results in linear dynamics, we will show that every dynamical system (X,f), where f is a continuous self-map on a separable metric space X, can be extended to a chaotic (in the sense of Devaney) dynamical system in an isometric way. 相似文献
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Ehud de Shalit 《Inventiones Mathematicae》1995,121(1):225-255
Under certain assumptions, we prove a conjecture of Mazur and Tate describing a relation between the modular symbol attached to an elliptic curve with split multiplicative reduction atp, and itsp-adic period. We generalize this relation to modular forms of weight 2 with coefficients not necessarily in.Oblatum 24-XI-1993 & 8-VI-1994 相似文献
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V. Yu. Tyshchenko 《Differential Equations》2010,46(5):758-761
We study the properties of invariants of discrete dynamical systems. The case in which discrete dynamical systems admit a discrete symmetry is considered. 相似文献
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《Chaos, solitons, and fractals》2001,12(11):2103-2108
A dynamical system motivated by discrete physics is studied. Fuzzy dynamical systems are used to study fuzzy discrete replicator dynamics of hawk–dove (HD) and prisoner's dilemma (PD) games. New solutions are obtained. Finally a preliminary study for fuzzy predator–prey model is studied and a new equilibrium is found. 相似文献
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Rémi Boutonnet 《Journal of Functional Analysis》2012,263(4):1040-1063
We investigate Gaussian actions through the study of their crossed-product von Neumann algebra. The motivational result is Chifan and Ioana?s ergodic decomposition theorem for Bernoulli actions (Chifan and Ioana, 2010 [4]) that we generalize to Gaussian actions (Theorem A). We also give general structural results (Theorems 3.4 and 3.8) that allow us to get a more accurate result at the level of von Neumann algebras. More precisely, for a large class of Gaussian actions , we show that any subfactor N of containing is either hyperfinite or is non-Gamma and prime. At the end of the article, we show a similar result for Bogoliubov actions. 相似文献
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《Chaos, solitons, and fractals》2005,23(4):1381-1384
Let (X, d) be a metric space and let f: (X, d) → (X, d) be a continuous map. In this note we investigate the relationships between the chaoticity of some set-valued discrete dynamical systems associated to f (collective chaos) and the chaoticity of f (individual chaos). 相似文献
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