Multifractal formalism for some parabolic maps

KENTARO NAKAISHI

doi:10.1017/S0143385700000456

Abstract

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We study multifractal spectra of a simple class of interval transformations with a neutral fixed point. The analyticity of their spectral curves depends on whether the absolutely continuous invariant measure is infinite or not.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Kesseböhmer, Marc and Stratmann, Bernd O 2007. A multifractal analysis for Stern-Brocot intervals, continued fractions and Diophantine growth rates. Journal für die reine und angewandte Mathematik (Crelles Journal), Vol. 2007, Issue. 605,

Barreira, Luis and Doutor, Paulo 2009. Dimension Spectra of Hyperbolic Flows. Journal of Statistical Physics, Vol. 136, Issue. 3, p. 505.

GELFERT, KATRIN and RAMS, MICHAŁ 2009. The Lyapunov spectrum of some parabolic systems. Ergodic Theory and Dynamical Systems, Vol. 29, Issue. 3, p. 919.

Johansson, Anders Jordan, Thomas M. Öberg, Anders and Pollicott, Mark 2010. Multifractal analysis of non-uniformly hyperbolic systems. Israel Journal of Mathematics, Vol. 177, Issue. 1, p. 125.

IOMMI, GODOFREDO 2010. Multifractal analysis of the Lyapunov exponent for the backward continued fraction map. Ergodic Theory and Dynamical Systems, Vol. 30, Issue. 1, p. 211.

Pacifico, Maria José and Todd, Mike 2010. Thermodynamic Formalism for Contracting Lorenz Flows. Journal of Statistical Physics, Vol. 139, Issue. 1, p. 159.

CHUNG, YONG MOO 2010. BIRKHOFF SPECTRA FOR ONE-DIMENSIONAL MAPS WITH SOME HYPERBOLICITY. Stochastics and Dynamics, Vol. 10, Issue. 01, p. 53.

JORDAN, THOMAS and RAMS, MICHAŁ 2011. Multifractal analysis of weak Gibbs measures for non-uniformly expanding C1 maps. Ergodic Theory and Dynamical Systems, Vol. 31, Issue. 1, p. 143.

CLIMENHAGA, VAUGHN 2011. Bowen’s equation in the non-uniform setting. Ergodic Theory and Dynamical Systems, Vol. 31, Issue. 4, p. 1163.

Iommi, Godofredo and Todd, Mike 2011. Dimension Theory for Multimodal Maps. Annales Henri Poincaré, Vol. 12, Issue. 3, p. 591.

Iommi, Godofredo and Todd, Mike 2013. Thermodynamic formalism for interval maps: inducing schemes. Dynamical Systems, Vol. 28, Issue. 3, p. 354.

Barreira, Luís 2013. Dimension Theory of Hyperbolic Flows. p. 1.

CLIMENHAGA, VAUGHN 2014. The thermodynamic approach to multifractal analysis. Ergodic Theory and Dynamical Systems, Vol. 34, Issue. 5, p. 1409.

CHUNG, YONG MOO and TAKAHASI, HIROKI 2014. Multifractal formalism for Benedicks–Carleson quadratic maps. Ergodic Theory and Dynamical Systems, Vol. 34, Issue. 4, p. 1116.

Iommi, Godofredo Jordan, Thomas and Todd, Mike 2015. Recurrence and transience for suspension flows. Israel Journal of Mathematics, Vol. 209, Issue. 2, p. 547.

Iommi, Godofredo Jordan, Thomas and Todd, Mike 2017. Transience and multifractal analysis. Annales de l'Institut Henri Poincaré C, Analyse non linéaire, Vol. 34, Issue. 2, p. 407.

Ye, Yuan-Ling 2017. Multifractal analysis of non-uniformly contracting iterated function systems. Nonlinearity, Vol. 30, Issue. 5, p. 1708.

TAKAHASI, HIROKI 2018. Lyapunov spectrum for Hénon-like maps at the first bifurcation. Ergodic Theory and Dynamical Systems, Vol. 38, Issue. 3, p. 1168.

Jordan, Thomas Munday, Sara and Sahlsten, Tuomas 2018. Stability and perturbations of countable Markov maps*. Nonlinearity, Vol. 31, Issue. 4, p. 1351.

Duvall, Jason 2020. Schmidt’s game and nonuniformly expanding interval maps. Nonlinearity, Vol. 33, Issue. 11, p. 5611.

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Multifractal formalism for some parabolic maps

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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Multifractal formalism for some parabolic maps

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