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Statistical mechanics is founded on the assumption that all accessible configurations of a system are equally likely. This requires dynamics that explore all states over time, known as ergodic dynamics. In isolated quantum systems, however,…
This paper addresses structures of state space in quasiperiodically forced dynamical systems. We develop a theory of ergodic partition of state space in a class of measure-preserving and dissipative flows, which is a natural extension of…
In this paper, we show that for several interesting systems beyond uniform hyperbolicity, any generic continuous function has a unique maximizing measure with zero entropy. In some cases, we also know that the maximizing measure has full…
In this work we obtain a new criterion to establish ergodicity and non-uniform hyperbolicity of smooth measures of diffeomorphisms. This method allows us to give a more accurate description of certain ergodic components. The use of this…
We endow the set of all invariant measures of a topological dynamical system with a metric $\bar{\rho}$, which induces a topology stronger than the the weak$^*$-topology. Then, we study the closedness of ergodic measures within a…
We consider the open set constructed by M. Shub in [42] of partially hyperbolic skew products on the space $\mathbb{T}^2\times \mathbb{T}^2$ whose non-wandering set is not stable. We show that there exists an open set $\mathcal{U}$ of such…
Entropy production is often interpreted as a proxy for microscopic disorder or environmental roughness in stochastic systems. We test this interpretation using controlled simulations of overdamped stochastic dynamics on curved surfaces in…
We study the occurrence of historical behavior for almost every point in the setting of skew products with one-dimensional fiber dynamics. Under suitable ergodic conditions, we establish that a weak form of the arcsine law leads to the…
This paper is aim to extend Kenneth R. Berg's findings on the maximal entropy theorem and the ergodicity of measure convolution to the case of surjective homomorphisms. We further explores dynamical systems under surjective homomorphism in…
In this article, we continue the structural study of factor maps betweeen symbolic dynamical systems and the relative thermodynamic formalism. Here, one is studying a factor map from a shift of finite type $X$ (equipped with a potential…
In this paper we establish a dichotomy for the ergodic measures of maximal entropy for partially hyperbolic diffeomorphisms with one-dimensional compact center leaves which are virtually skew products over (transitive) Anosov homeomorphism.…
The interplay between activity and elasticity often found in active and living systems triggers a plethora of autonomous behaviors ranging from self-assembly and collective motion to actuation. Amongst these, spontaneous self-oscillations…
The statistical properties of mostly expanding partially hyperbolic diffeomorphisms have been substantially studied. In this paper, we would like to address the entropy properties of mostly expanding partially hyperbolic diffeomorphisms. We…
We extend the Nonconventional Ergodic Theorem for generic measures by Furstenberg, to several situations of interest arising from quantum dynamical systems. We deal with the diagonal state canonically associated to the product state (i.e.…
In this paper we study the anti-integrable limit scenario of skew-product systems. We consider a generalization of such systems based on the Frenkel-Kontorova model, and prove the existence of orbits with any fibered rotation number in…
We present an extension of the ergodic, mixing, and Bernoulli levels of the ergodic hierarchy for statistical models on curved manifolds, making use of elements of the information geometry. This extension focuses on the notion of…
We study two properties of nonsingular and infinite measure-preserving ergodic systems: weak double ergodicity, and ergodicity with isometric coefficients. We show that there exist infinite measure-preserving transformations that are…
Convergence extension, the simultaneous elongation of tissue along one axis while narrowing along a perpendicular axis, occurs during embryonic development. A fundamental process that contributes to shaping the organism, it happens in many…
We discuss recurrence and ergodicity properties of random walks and associated skew products for large classes of locally compact groups and homogeneous spaces. In particular we show that a closed subgroup of a product of finitely many…
In this paper, we establish a variational principle, between the fiber Bowen's topological entropy on conditional level sets of Birkhoff average and fiber measure-theoretical entropy, for the skew product transformation driven by a uniquely…