Related papers: Equilibrium states for hyperbolic potentials via i…

We construct symbolic dynamics for three dimensional flows with positive speed. More precisely, for each $\chi>0$, we code a set of full measure for every invariant probability measure which is $\chi$-hyperbolic. These include all ergodic…

We construct inducing schemes for general multi-dimensional piecewise expanding maps where the base transformation is Gibbs-Markov and the return times have exponential tails. Such structures are a crucial tool in proving statistical…

We study ergodic properties of partially hyperbolic systems whose central direction is mostly contracting. Earlier work of Bonatti, Viana about existence and finitude of physical measures is extended to the case of local diffeomorphisms.…

For hyperbolic first-order systems of linear partial differential equations (master equations), appearing in description of kinetic processes in physics, biology and chemistry we propose a new procedure to obtain their complete closed-form…

We introduce a class of continuous maps f of a compact metric space I admitting inducing schemes and describe the tower constructions associated with them. We then establish a thermodynamical formalism, i.e., describe a class of real-valued…

We introduce a general framework for the construction of well-balanced finite volume methods for hyperbolic balance laws. We use the phrase well-balancing in a broader sense, since our proposed method can be applied to exactly follow any…

We prove the existence of equilibrium states for partially hyperbolic endomorphisms with one-dimensional center bundle. We also prove, regarding a class of potentials, the uniqueness of such measures for endomorphisms defined on the 2-torus…

This work presents a novel family of well-balanced numerical schemes for hyperbolic systems of balance laws based on the kinetic relaxation approach. The method begins by transforming the original non-linear system into a linearized kinetic…

We investigate dynamical systems obtained by coupling two maps, one of which is chaotic and is exemplified by an Anosov diffeomorphism, and the other is of gradient type and is exemplified by a N-pole-to-S-pole map of the circle. Leveraging…

Symbolic dynamics, which partitions an infinite number of finite-length trajectories into a finite number of trajectory sets, describes the dynamics of a system in a simplified and coarse-grained way with a limited number of symbols. The…

For an ergodic hyperbolic measure $\omega$ of a $C^{1+{\alpha}}$ diffeomorphism, there is an $\omega$ full-measured set $\tilde\Lambda$ such that every nonempty, compact and connected subset $V$ of $\mathbb{M}_{inv}(\tilde\Lambda)$…

This paper deals with mathematical models of continuous crystallization described by hyperbolic systems of partial differential equations coupled with ordinary and integro-differential equations. The considered systems admit nonzero…

In this paper we study the thermodynamic formalism of strongly transitive endomorphisms $f$, focusing on the set all expanding measures. In case $f$ is a non-flat $C^{1+}$ map defined on a Riemannian manifold, these are invariant…

We study stable conditional measures for a certain equilibrium measure for hyperbolic endomorphisms, on basic sets with overlaps; we show that these conditional measures are geometric probabilities and measures of maximal stable dimension.…

We address the problem of existence and uniqueness (finite- ness) of ergodic equilibrium states for a natural class of partially hyperbolic dynamics homotopic to Anosov. We propose to study the disintegration of equilibrium states along…

In this paper, we show the uniqueness of equilibrium state for a family of partially hyperbolic horseshoes, introduced in [12] for some classes of continuous potentials. For the first class, the method used here is making use of the Sarig's…

This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of…

We study the optimization of ergodic averages for multi-valued dynamical systems, i.e. where points may have multiple different forward orbits. Under upper semi-continuity assumptions, we show that the maximum space average with respect to…

We study transitive step skew-product maps modeled over a complete shift of $k$, $k\ge2$, symbols whose fiber maps are defined on the circle and have intermingled contracting and expanding regions. These dynamics are genuinely nonhyperbolic…

In this work we obtain mixing (and in some cases sharp mixing rates) for a reasonable large class of invertible systems preserving an infinite measure. The examples considered here are the invertible analogue of both Markov and non Markov…