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On the Lagrange and Markov dynamical spectra

Published online by Cambridge University Press:  11 April 2016

SERGIO AUGUSTO ROMAÑA IBARRA  and
CARLOS GUSTAVO T. DE A. MOREIRA
SERGIO AUGUSTO ROMAÑA IBARRA
Affiliation:
Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Centro de Tecnologia - Bloco C - Cidade Universitária Ilha do Fundão, cep 21941-909, Rio de Janeiro, Brasil email [email protected]
CARLOS GUSTAVO T. DE A. MOREIRA
Affiliation:
Instituto Nacional de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina 110, cep 22460-320, Rio de Janeiro, Brasil email [email protected]
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Abstract

We consider the Lagrange and the Markov dynamical spectra associated to horseshoes on a surface with Hausdorff dimension greater than one. We show that for a ‘large’ set of real functions on the surface and for ‘typical’ horseshoes with Hausdorff dimension greater than one, both the Lagrange and the Markov dynamical spectra have persistently non-empty interior.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 37 , Issue 5 , August 2017 , pp. 1570 - 1591
Copyright
© Cambridge University Press, 2016 

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