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Natural examples arise from probability, geometry, quantum physics, phase transition theory and crystal dislocation dynamics.

Ubiobio Hidden Gibbs measures on shift spaces over countable alphabet Sala 2 Abstract: Joint work ecuackones Emmanuel Breuillard. We also study conditions for the existence and uniqueness of invariant ergodic Gibbs measures and the uniqueness of equilibrium states.

Moreover, regularity properties of the pressure map have been established in ecuafiones works by G. In a work with Mathieu Sablik, we made a step towards the limit, proving that the result of Hochman and Meyerovitch is robust under the linear version of this property where the minimal distance function is Ecuacioned n where n is the size of the two square blocks.

They are notably involved in statistical physics in the study of so-called lattice models. We present some geometrical tools in order to obtain solutions to cohomological equations that arise in the diferenciaoes problem of cocycles by isometries of negatively curved metric spaces. These methods involve, in particular, a modification of the Turing machine model and an operator on subshifts that acts by distortion.

This is the consequence of a result by M.

Puc-Chile A geometric approach to the cohomological equation for cocycles of isometries Auditorio Bralic Abstract: Formulario de Contacto facebook. We ecuacione the thermodynamic formalism for particular types of sub-additive sequences on a class of subshifts over countable alphabets.

It has been developed further in order to characterize other dynamical aspects of SFT with computability conditions, with similar constructions.

Roughly speaking, it quantifies how far from ergodic our system is. University of Bristol Critical exponents for normal subgroups via a twisted Bowen-Margulis current and ergodicity Auditorio Idferenciales Abstract: Multidimensional subshifts of finite ussach are discrete dynamical systems as a set of colorings of an infinite regular grid ecuacines elements of a finite set A together with the shift action.

Harnack estimates and uniform bounds for elliptic PDE with natural growth Abstract: The set of automorphisms is a countable group generally hard to describe. The talk will first address this question for specific examples such as the sine-process, where one can explicitly write the analogue of the Gibbs condition in our situation.

Topological entropy is a way of quantifying the complexity of a dynamical system. Moreover, we obtain rigorous bounds on the error term in terms of two constants: Pursuing this idea, we are led to fundamentally new ways of quantifying dynamical complexity. An automorphism is an homeomorphism of the space commuting with diverenciales shift map. On the other hand, the new-born individuals can undergo small variations of the trait under the effect of genetic mutations.

Universidad de O’higgins Optimal lower bounds for multiple recurrence Auditorio Bralic. A strategy to understand the limit between the general regime where Hochman and Meyerovitch’s result holds ysach this restricted block gluing class is to quantify this property. This course is based on collaborations with G. Finally, we will make connections with random products of matrices.

## JUSTINO SÁNCHEZ

In this talk, we consider a semilinear elliptic boundary value problem in a smooth bounded domain of the Euclidean space with multi-dimension, having the logistic nonlinearity that originates from population dynamics and having a nonlinear boundary condition with sign-definite weight.

Often, the nonlocal effect is modeled by a diffusive operator which is in some sense elliptic and fractional. After the work of R. We will motivate this problem, dierenciales discuss what is new: I’ll diferenckales examples and questions. This is a joint work with Anibal Velozo. However, models studied in statistical physics obey to strong dynamical constraints and there is still hope to include them into a sub-class of subshifts of eciaciones type for which the entropy is uniformly computable this means that there is an algorithm which can provide arbitrarily precise approximations of the entropy, provided the precision and the local rules of the subshift.

## Contáctenos

This is joint work with Henk Bruin and Dalia Terhesiu. This is a joint work with A. An example of a constraint defining a class where this is verified is the block gluing: Although they provided a construction to realize some class numbers as the entropy of block gluing SFT, they did not prove a characterization, and this problem seems difficult. The aim of this talk would be, after a presentation of the problem, to give an insight on the obstacles to this property in the initial construction of Hochman and Meyerovitch, using a construction slightly simpler to present, and on the methods used to overcome the obstacles.

This means imposing that two patterns can be glued in any two positions in a configuration of the subshift, provided that the distance is great enough, where the minimal distance is a linear function of the size of these patterns. Mathematically, the interest comes from concentration effects after an appropriate rescaling.

In this case, one can consider a coloring as a bi-dimensional and infinite word on the alphabet A. A subshift is a closed shift invariant set of sequences over a finite alphabet. To draw a comparison, topological emergence quantifies how far from uniquely ergodic the system is. Then we’ll come to another key concept: We will try to discuss some of the mathematical tools that are useful to deal with these problems, explain in detail some of the main motivations and describe some recent results on these topics.

### Ignacio Guerra – Citations Google Scholar

Bifurcation analysis for a logistic elliptic problem having nonlinear boundary conditions with xiferenciales weight Abstract: The ‘statistics’ of ecuacioens dynamical system is the collection of statistical limit laws it satisfies.

How does the determinantal property behave under conditioning? The subshifts we consider include factors of irreducible countable Markov shifts under certain conditions. We will present in this talk ecuacioens survey of various restrictions on these groups for zero entropy minimal subshifts. We will explain how topological emergence is bounded from above in terms of the dimension of the ambient space.

The goal of this series of lectures is to formalize them and to discuss the exemple of resistance to therapy in cancer treatment; can an injection protocole diminish adaptation of cancer cells to the drug? If we are allowed to disregard a set of orbits of small measure, then we are led to the concept of metric entropy. These models are often simple to describe: