In this paper we prove a multifractal formalism of Birkhoff averages for interval maps with countably many branches. Furthermore, that under certain regularity assumptions on the potential spectrum is real analytic. Applications these results to number theory are also given. Finally, compute Hausdorff dimension set points which average infinite.

Abstract For a class of potentials $\psi $ satisfying condition depending on the roof function suspension (semi)flow, we show an EKP inequality, which can be interpreted as Hölder continuity property in weak ${^*}$ norm measures, with respect to pressure those where exponent depends $L^q$ -space belongs. This also captures new type phase transition for intermittent (semi)flows (and maps).

We investigate various relaxations of additivity for set maps into Banach spaces in the context representations amenable groups. Specifically, we establish conditions under which asymptotically additive and almost are equivalent. For lattices, further show that these notions related to a third weak form adapted order structure space. By utilizing equivalences reducing non-additive settings one by finding suitable realizations, derive new ergodic theorems group streamline proofs existing...

Abstract We extend the theory of transience to general dynamical systems with no Markov structure assumed. This is linked phase transitions. also provide new examples illustrate different kinds transient behaviour.

We study the multifractal analysis of pointwise dimension for equilibrium measures on countable Markov shifts. The main difficulty is that space not compact. In order to overcome this, we use an approximation argument based theory convergence Fenchel pairs developed by Wijsman. results Pesin and Weiss compact spaces are used as well. also prove a Bowen formula It turns out that, in this setting, provides Hausdorff set recurrent points.

We introduce a definition of pressure for almost-additive sequences continuous functions defined over (non-compact) countable Markov shifts. The variational principle is proved. Under certain assumptions we prove the existence Gibbs and equilibrium measures. Applications are given to study maximal Lypaunov exponents product matrices.

Abstract In this paper we study the multifractal spectrum of Lyapunov exponents for interval maps with infinitely many branches and a parabolic fixed point. It turns out that, in strong contrast hyperbolic case, domain is unbounded points non-differentiability might exist. Moreover, not concave. We establish conditions that ensure existence inflection points. To best our knowledge first time type have been given. also thermodynamic formalism such maps. prove pressure function real analytic...

Abstract This survey paper concerns inducing schemes in the context of interval maps. We explain how study these induced systems allows for fine description not only thermodynamic formalism certain multimodal maps, but also its multifractal structure. Keywords: equilibrium statesthermodynamic formalismmultimodal mapsmultifractal analysis Acknowledgements The authors would like to thank H. Bruin, K. Gelfert, L. Olsen, I. Petrykiewicz, J. Rivera-Letelier and referee their useful comments. GI...

Journal Article Multifractal Analysis for Quotients of Birkhoff Sums Countable Markov Maps Get access Godofredo Iommi, Iommi 1Facultad de Matemáticas, Pontificia Universidad Católica Chile (PUC), Avenida Vicuña Mackenna 4860, Santiago, Correspondence to be sent to: giommi@mat.puc.cl URL: http://www.mat.puc.cl/~giommi/ Search other works by this author on: Oxford Academic Google Scholar Thomas Jordan 2The School Mathematics, The University Bristol, Walk, Clifton, Bristol BS8 1TW, UK...

In this note we prove that every weak Gibbs measure for an asymptotically additive sequence is a another sequence. particular, continuous potential This allows us, example, to apply recent results on dimension theory of sequences study multifractal analysis potentials.

We prove that the entropy map for countable Markov shifts of finite is upper semi-continuous on set ergodic measures.Note phase space non-compact.We also discuss related problem existence measures maximal entropy.

For each real number, we obtain an asymptotic for the number of partial quotients in continued fraction expansion that can be obtained from first n terms its β-expansion. A novelty our approach is use methods theory dynamical systems.