Browsing by Author "Iommi, Godofredo"
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- ItemEntropy in the cusp and phase transitions for geodesic flows(2018) Iommi, Godofredo; Riquelme, Felipe; Velozo, Anibal
- ItemFrequency of digits in the Luroth expansion(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2009) Barreira, Luis; Iommi, GodofredoIn this note we consider the Luroth expansion of a real number, and we Study the Hausdorff dimension of a class of sets defined in terms of the frequencies of digits in the expansion. We also study the speed at which the approximants obtained from the Luroth expansion converge. In addition, we describe the multifractal properties of the level sets of the Lyapunov exponent, which measures the exponential speed of approximation obtained from the approximants. Finally, we describe the relation of the Luroth expansion with the continued fraction expansion and the beta-expansion. We remark that our work is still another application of the theory of dynamical systems to number theory. (C) 2008 Elsevier Inc. All rights reserved.
- ItemMeasures of maximal entropy for suspension flows(2020) Iommi, Godofredo; Velozo, A.
- ItemMultifractal Analysis for Quotients of Birkhoff Sums for Countable Markov Maps(2015) Iommi, Godofredo; Jordán, Thomas
- ItemMultifractal analysis of Birkhoff averages for countable Markov maps(2015) Iommi, Godofredo; Jordán, Thomas
- ItemMultifractal analysis of the Lyapunov exponent for the backward continued fraction map(CAMBRIDGE UNIV PRESS, 2010) Iommi, GodofredoIn 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 with the hyperbolic case, the domain of the spectrum is unbounded and points of non-differentiability might exist. Moreover, the spectrum is not concave. We establish conditions that ensure the existence of inflection points. To the best of our knowledge this is the first time that conditions of this type have been given. We also study the thermodynamic formalism for such maps. We prove that the pressure function is real analytic in a certain interval and then becomes equal to zero. We also discuss the existence and uniqueness of equilibrium measures. In order to do so, we introduce a family of countable Markov shifts that can be thought of as a generalization of the renewal shift.
- ItemEl Pacífico Latinoamericano = The Latin American Pacific.(2009) Cruz C., Carlos Alberto; Iommi, Godofredo
- ItemPartial quotients of continued fractions and beta-expansions(IOP PUBLISHING LTD, 2008) Barreira, Luis; Iommi, GodofredoFor each real number, we obtain an asymptotic for the number of partial quotients in the continued fraction expansion that can be obtained from the first n terms of its beta-expansion. A novelty of our approach is the use of methods of the theory of dynamical systems.
- ItemPhase Transitions for Suspension Flows(2013) Iommi, Godofredo; Jordan, T.
- ItemPressure, Poincare series and box dimension of the boundary(IOP PUBLISHING LTD, 2021) Iommi, Godofredo; Velozo, AnibalIn this note we prove two related results. First, we show that for certain Markov interval maps with infinitely many branches the upper box dimension of the boundary can be read from the pressure of the geometric potential. Secondly, we prove that the box dimension of the set of iterates of a point in partial differential Hn
- ItemRecurrence and transience for suspension flows(2015) Iommi, Godofredo; Jordán, Thomas; Todd, Mike
- ItemSome applications of thermodynamic formalism to numerical systems(2021) Contreras, Erik; Iommi, Godofredo; Pontificia Universidad Católica de Chile. Facultad de Matemáticas
- ItemThe Lyapunov spectrum as the Newton method(ELSEVIER SCIENCE BV, 2012) Iommi, GodofredoFor a class of dynamical systems, the cookie-cutter maps, we prove that the Lyapunov spectrum coincides with the map given by the Newton-Raphson method applied to the derivative of the pressure function. (C) 2012 Elsevier B.V. All rights reserved.
- ItemThe scaling mean and a Law of Large Permanents(2016) Bochi, Jairo; Iommi, Godofredo; Ponce Acevedo, Mario
- ItemThermodynamic formalism for interval maps : Inducing schemes(2013) Iommi, Godofredo; Todd, M.
- ItemTime change for flows and thermodynamic formalism(2019) Cipriano, I.; Iommi, Godofredo
- ItemTransience and multifractal analysis(2017) Iommi, Godofredo; Jordan, Thomas; Todd, Mike
- ItemTransience in dynamical systems(2013) Iommi, Godofredo; Todd, M.
- ItemWEAK GIBBS MEASURES AS GIBBS MEASURES FOR ASYMPTOTICALLY ADDITIVE SEQUENCES(2017) Iommi, Godofredo; Yayama, Y.
- ItemZero Temperature Limits of Gibbs States for Almost-Additive Potentials(2014) Iommi, Godofredo; Yayama, Y.