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[GIKN] and [BBD1] propose two very different ways for building non hyperbolic measures, [GIKN] building such a measure as the limit of periodic measures and [BBD1] as the $\omega$-limit set of a single orbit, with a uniformly vanishing…

In this Letter, we clarify the physical origin of effective transport in periodic and tilted periodic systems. When Brownian dynamics is examined on the scale of a single period, the particle displacement admits a natural separation into a…

Driven diffusive systems have provided simple models for non-equilibrium systems with non-trivial structures. Steady state behaviour of these systems with constant boundary conditions have been studied extensively. Comparatively less work…

We give a classification of generic coadjoint orbits for the group of area-preserving diffeomorphisms of a closed non-orientable surface. This completes V. Arnold's program of studying invariants of incompressible fluids in 2D. As an…

In a previous paper the \textit{real} evolution of the system of ODEs \ddot{z}_{n} + z_{n}=\sum\limits_{m = 1, m \ne n}^{N} g_{nm}{(z_{n} - z_{m})} ^{- 3}, z_{n} \equiv z_{n}(t), \qquad \dot {z}_{n} \equiv \frac{d z_{n}(t)}{dt}, \qquad n =…

This paper studies nonstationary open dynamical systems from the statistical viewpoint. By open, we mean that trajectories may escape through holes in the phase space. By nonstationary, we mean that the dynamical model itself (as well as…

Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…

We consider the noise-induced transitions in the randomly perturbed discrete logistic map from a linearly stable periodic orbit consisting of T periodic points. The traditional large deviation theory and asymptotic analysis for small noise…

We study (topological) pseudo-Anosov flows from the perspective of the associated group actions on their orbit spaces and boundary at infinity. We extend the definition of Anosov-like action from [BFM22] from the transitive to the general…

The main objective of this paper is twofold. We first show that if the doubly-weighted Bohr spectrum of an almost periodic function exists, then it is either empty or coincides with the Bohr spectrum of that function. Next, we investigate…

This paper gives an overview of recent results concerning the long time dynamics of repeated interaction quantum systems in a deterministic and random framework. We describe the non equilibrium steady states (NESS) such systems display and…

The existence and multiplicity of positive periodic solutions for second order non-autonomous singular dynamical systems are established with superlinearity or sublinearity assumptions at infinity for an appropriately chosen parameter. Our…

Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final…

By folding an autonomous system of rational equations in the plane to a scalar difference equation, we show that the rational system has coexisting periodic orbits of all possible periods as well as stable aperiodic orbits for certain…

We study connected branches of non-constant {$2\pi$-pe}riodic solutions of the Hamilton equation \begin{displaymath} \dot{x}(t)=\lambda J\nabla H(x(t)), \end{displaymath} where $\lambda\in\halfline,$ $H\in C^2(\R^n\times\R^n,\R)$ and $…

In this paper we study the properties of the periodic orbits of \"x + V'_x(t, x) = 0 with x \in S1 and V(t, x) a T0 periodic potential. Called {\rho} \in (1/T0)Q the frequency of windings of an orbit in S1 we show that exists an infinite…

We discuss the dynamics beyond topological hyperbolicity considering homeomorphisms satisfying the shadowing property and generalizations of expansivity. It is proved that transitive countably expansive homeomorphisms satisfying the…

In this paper we give a concept of multi-dimensional-time dynamical system (MDTDS). Such dynamical system is generated by a finite family of functions $\{f_i\}$. The multi-dimensional-time space is taken as a free group. Using the subgroups…

We obtain an asymptotic formula for the number of pairs of closed orbits of a weak-mixing transitive Anosov flow whose homology classes have a fixed difference.

Random substitutions are a natural generalisation of their classical `deterministic' counterpart, whereby at every step of iterating the substitution, instead of replacing a letter with a predetermined word, every letter is independently…