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VOL. 53 | 2009 Discrete potential theory for iterated maps of the interval
C. Correia Ramos, Nuno Martins, J. Sousa Ramos, Ricardo Severino

Editor(s) Saber Elaydi, Kazuo Nishimura, Mitsuhiro Shishikura, Nobuyuki Tose

Abstract

Using Markov partitions and algebraic graph theory we introduce, in the context of discrete dynamical systems, some laws which characterize the nonlinear dynamics of iterated maps of the interval. In the Markov digraphs we assume that each directed edge has a weight associated to it, given by the Markov invariant measure. This system of weights produces a diffusion process determined by a transition matrix. In this setting, we define a current and a potential which are dynamical invariants.

Information

Published: 1 January 2009
First available in Project Euclid: 28 November 2018

zbMATH: 1185.37098
MathSciNet: MR2582411

Digital Object Identifier: 10.2969/aspm/05310121

Rights: Copyright © 2009 Mathematical Society of Japan

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