Related papers: Renormalisation-induced phase transitions for unim…
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…
The thermodynamic formalism for dynamical systems with many degrees of freedom is extended to deal with time averages and fluctuations of some macroscopic quantity along typical orbits, and applied to coupled map lattices exhibiting phase…
For a smooth map f of a compact interval I admitting an inducing scheme we establish a thermodynamical formalism, i.e., describe a class of real-valued potential functions $\phi$ on I which admit a unique equilibrium measure $\mu_\phi$. Our…
In this paper we give a combinatorial description of the renormlization limits of infinitely renormalizable unimodal maps with {\it essentially bounded} combinatorics admitting quadratic-like complex extensions. As an application we…
This article characterizes phase transitions in temperature within a specific space of H\"older continuous potentials, distinguished by their regularity and asymptotic behavior at zero. We also characterize the phase transitions in…
We consider infinitely renormalizable unimodal mappings with topological type which is periodic under renormalization. We study the limiting behavior of fixed points of the renormalization operator as the order of the critical point…
This survey article concerns inducing schemes in the context of interval maps. We explain how the study of these induced systems allows for the fine description of, not only, the thermodynamic formalism for certain multimodal maps, but also…
In the theory of renormalization for classical dynamical systems, e.g. unimodal maps and critical circle maps, topological conjugacy classes are stable manifolds of renormalization. Physically more realistic systems on the other hand may…
The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium, that have yet to relax to a steady state. A relation between information, escape rate, and the…
We examine thermodynamic formalism for a class of renormalizable dynamical systems which in the symbolic space is generated by the Thue-Morse substitution, and in complex dynamics by the Feigenbaum-Coullet-Tresser map. The basic question…
We study a one-parameter family of countably piecewise linear interval maps, which, although Markov, fail the `large image property'. This leads to conservative as well as dissipative behaviour for different maps in the family with respect…
We give the first example of a quadratic map having a phase transition after the first zero of the geometric pressure function. This implies that several dimension spectra and large deviation rate functions associated to this map are not…
Phase transitions are ubiquitous across life, yet hard to quantify and describe accurately. In this work, we develop an approach for characterizing generic attributes of phase transitions from very limited observations made deep within…
Inverse phase transitions are striking phenomena in which an apparently more ordered state disorders under cooling. This behavior can naturally emerge in tricritical systems on heterogeneous networks and it is strongly enhanced by the…
We show that the topological entropy is monotonic for unimodal interval maps which are obtained from the restriction of quadratic rational maps with real coefficients. This is done by ruling out the existence of certain post-critical curves…
We consider the thermodynamic formalism of a complex rational map $f$ of degree at least two, viewed as a dynamical system acting on the Riemann sphere. More precisely, for a real parameter $t$ we study the (non-)existence of equilibrium…
This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function…
We study circle maps with a flat interval where the critical exponents at the two boundary points of the flat spot might be different. The space of such systems is partitioned in two connected parts whose common boundary only depends on the…
We define an analytic setting for renormalization of unimodal maps with an arbitrary critical exponent. We prove the global Hyperbolicity of Renormalization conjecture for unimodal maps of bounded type with a critical exponent which is…
We study the dynamics of the renormalization operator for multimodal maps. In particular, we prove the exponential convergence of this operator for infinitely renormalizable maps with same bounded combinatorial type.