Please use this identifier to cite or link to this item:
http://hdl.handle.net/10174/31307
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Title: | Markov invariant dynamics |
Authors: | Correia Ramos, Carlos |
Keywords: | Invariant dynamics Primitive matrices Symbolic dynamics Interval maps Markov partitions State splitting |
Issue Date: | 1-Jul-2021 |
Publisher: | Elsevier |
Citation: | C. Correia Ramos, N. Martins, P.R. Pinto,
Markov invariant dynamics,
Linear Algebra and its Applications,
Volume 620,
2021,
Pages 268-296,
ISSN 0024-3795,
https://doi.org/10.1016/j.laa.2021.02.028. |
Abstract: | We consider, , a certain class of Markov interval maps with domain contained in the interval I, whose associated transition matrix , necessarily primitive, plays a crucial role in the study of the underlying dynamics.
We study the problem of deciding when a restriction of a map to a subset is in the class , where is the minimal closed interval containing J. We establish natural conditions on so that is a Markov map. Then we tackle the central problem of deciding when the matrix is primitive in this framework. We are able to enumerate the sets J, satisfying the referred conditions, through a systematic process of elimination of the rows/columns of the state splitting of associated to the so called removable states, which ensures the primitivity of the matrices . |
URI: | https://www.sciencedirect.com/science/article/abs/pii/S0024379521000951?via%3Dihub http://hdl.handle.net/10174/31307 |
Type: | article |
Appears in Collections: | MAT - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica CIMA - Publicações - Artigos em Revistas Internacionais Com Arbitragem Científica
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