arXiv subjects

Godofredo Iommi

Publications and source records attributed to Godofredo Iommi.

39 records · Page 3Linked to original sources

arXiv2009

Natural equilibrium states for multimodal maps

This paper is devoted to the study of the thermodynamic formalism for a class of real multimodal maps. This class contains, but it is larger than, Collet-Eckmann. For a map in this class, we prove existence and uniqueness of equilibrium states for the geometric potentials $-t \log|Df|$, for the largest possible interval of parameters $t$. We also study the regularity and convexity properties of the pressure function, completely characterising the first order phase transitions. Results concerning the existence of absolutely continuous invariant measures with respect to the Lebesgue measure are also obtained.

math.DS↗

arXiv2008

The Lyapunov spectrum is not always concave

We characterize one-dimensional compact repellers having nonconcave Lyapunov spectra. For linear maps with two branches we give an explicit condition that characterizes non-concave Lyapunov spectra.

math.DS↗

arXiv2008

Multifractal analysis of Lyapunov exponent for the backward continued fraction map

In this note 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. We also study the thermodynamic formalism for such maps. We prove that the pressure function is real analytic in a certain interval and then it becomes equal to zero.

math.DS↗