9 papers
Thermodynamic formalism and multifractal analysis of Birkhoff averages for parabolic rational maps
Yuya Arima
In this paper, we study the multifractal analysis of Birkhoff averages for parabolic rational maps. We establish a conditional variational principle and prove the real analyticity…
Existence of the Lyapunov exponent for -unimodal maps
Yuya Arima
In this paper, we show that for any -unimodal map on with a non-flat critical point the Lyapunov exponent exists for Lebesgue almost every point and is equal to a co…
Linear response asymmetry between SRB and physical measures for families of intermittent maps with a transition point
Yuya Arima
We study linear response for families of intermittent maps whose SRB measure undergoes a transition from finite to infinite total mass at a critical parameter value. Our results re…
Thermodynamic formalism and multifractal analysis of Birkhoff averages for non-uniformly expanding Rényi interval maps with countably many branches
Yuya Arima
In this paper, we study the multifractal spectrum of Birkhoff averages for non-uniformly expanding Rényi interval maps with countably many branches. Our main theorem substantially…
Thermodynamic formalism and multifractal analysis of Birkhoff averages for non-uniformly expanding interval maps with finitely many branches
Yuya Arima
In this paper, we perform a multifractal analysis of Birkhoff averages for interval maps with finitely many branches and parabolic fixed points. Using the thermodynamic approach, w…
Bowen's formula and the difference between random iterated function systems and random recursive constructions
Yuya Arima
In this paper, we show that the difference in independence structures between random iterated function systems and random recursive constructions is reflected in the validity of Bo…
Multifractal analysis of the Lyapunov exponent for random graph directed Markov systems
Yuya Arima
In this paper, we perform the multifractal analysis of the Lyapunov exponent for random conformal graph directed Markov systems introduced by Roy and Urbański (2011). We also gener…
Polynomial convergence rate at infinity for the cusp winding spectrum of generalized Schottky groups
Yuya Arima
We show that the convergence rate of the cusp winding spectrum to the Hausdorff dimension of the limit set of a generalized Schottky group with one parabolic generator is polynomia…
Higher-dimensional multifractal analysis for the cusp winding process on hyperbolic surfaces
Yuya Arima
We perform a multifractal analysis of the growth rate of the number of cusp windings for the geodesic flow on hyperbolic surfaces with cusps. Our main theorem establishe…