p-Adic (3, 2)-rational dynamical systems

Sattarov, I. A.

doi:10.1134/s2070046615010045

Cited by 14 publications

(3 citation statements)

References 31 publications

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“…In [1], [7], [8] and [9] the trajectories of some rational p-adic dynamical systems in a complex p-adic field C p are studied.…”

Section: Introductionmentioning

confidence: 99%

Ergodicity Properties of p-Adic (2, 1)-Rational Dynamical Systems with Unique Fixed Point

Sattarov¹

2018

Springer Proceedings in Mathematics &Amp; Statistics

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We consider a family of (2, 1)-rational functions given on the set of padic field Q p . Each such function has a unique fixed point. We study ergodicity properties of the dynamical systems generated by (2, 1)-rational functions. For each such function we describe all possible invariant spheres. We characterize ergodicity of each p-adic dynamical system with respect to Haar measure reduced on each invariant sphere. In particular, we found an invariant spheres on which the dynamical system is ergodic and on all other invariant spheres the dynamical systems are not ergodic.

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“…In [1], [7], [8] and [9] the trajectories of some rational p-adic dynamical systems in a complex p-adic field C p are studied.…”

Section: Introductionmentioning

confidence: 99%

Ergodicity Properties of p-Adic (2, 1)-Rational Dynamical Systems with Unique Fixed Point

Sattarov¹

2018

Springer Proceedings in Mathematics &Amp; Statistics

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“…The dynamical properties of the fixed points of the rational maps have been studied in the space C p of p-adic complex numbers [5,23,24,28] and in the adelic space [10]. The Fatou and Julia theory of the rational maps on C p , and on the Berkovich space over C p , are also developed [7,6,20,26,27].…”

Section: Introductionmentioning

confidence: 99%

Minimality of <i>p</i>-adic rational maps with good reduction

Fan

Liao

et al. 2017

Discrete &Amp; Continuous Dynamical Systems - A

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A rational map with good reduction in the field Qp of p-adic numbers defines a 1-Lipschitz dynamical system on the projective line P 1 (Qp) over Qp. The dynamical structure of such a system is completely described by a minimal decomposition. That is to say, P 1 (Qp) is decomposed into three parts: finitely many periodic orbits; finite or countably many minimal subsystems each consisting of a finite union of balls; and the attracting basins of periodic orbits and minimal subsystems. For any prime p, a criterion of minimality for rational maps with good reduction is obtained. When p = 2, a condition in terms of the coefficients of the rational map is proved to be necessary for the map being minimal and having good reduction, and sufficient for the map being minimal and 1-Lipschitz. It is also proved that a rational map having good reduction of degree 2, 3 and 4 can never be minimal on the whole space P 1 (Q 2 ).

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“…On the other side, the dynamical properties of the fixed points of the rational maps have been studied in the space C p of p-adic complex numbers [4,21,23,27] and in the adelic space [8]. The Fatou and Julia theory of the rational maps on C p , and on the Berkovich space over C p , are also developed [6,5,19,25,26].…”

Section: Introductionmentioning

confidence: 99%

Rational map $ax+1/x$ on the projective line over $\mathbb{Q}\_{p}$

Fan,

Liao

2016

Preprint

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p-Adic (3, 2)-rational dynamical systems

Cited by 14 publications

References 31 publications

Ergodicity Properties of p-Adic (2, 1)-Rational Dynamical Systems with Unique Fixed Point

Ergodicity Properties of p-Adic (2, 1)-Rational Dynamical Systems with Unique Fixed Point

Minimality of <i>p</i>-adic rational maps with good reduction

Rational map $ax+1/x$ on the projective line over $\mathbb{Q}\_{p}$

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