Advanced Studies in Pure Mathematics

Discrete potential theory for iterated maps of the interval

C. Correia Ramos, Nuno Martins, J. Sousa Ramos, and Ricardo Severino

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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.

Article information

Source
Advances in Discrete Dynamical Systems, S. Elaydi, K. Nishimura, M. Shishikura and N. Tose, eds. (Tokyo: Mathematical Society of Japan, 2009), 121-128

Dates
Received: 15 November 2006
Revised: 12 October 2007
First available in Project Euclid: 28 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543447647

Digital Object Identifier
doi:10.2969/aspm/05310121

Mathematical Reviews number (MathSciNet)
MR2582411

Zentralblatt MATH identifier
1185.37098

Citation

Ramos, C. Correia; Martins, Nuno; Ramos, J. Sousa; Severino, Ricardo. Discrete potential theory for iterated maps of the interval. Advances in Discrete Dynamical Systems, 121--128, Mathematical Society of Japan, Tokyo, Japan, 2009. doi:10.2969/aspm/05310121. https://projecteuclid.org/euclid.aspm/1543447647


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