Related papers: Non-autonomous dynamics of holomorphic mappings in…
Relatively independent joinings of W*-dynamical systems are constructed. This is intimately related to subsystems of W*-dynamical systems, and therefore we also study general properties of subsystems, in particular fixed point subsystems…
In this short note, we investigate non-invertible stochastic dynamical systems on the unit interval $[0, 1]$. We provide a handy condition for unique ergodicity for systems that are injective in mean. On the other hand, we give concrete…
We study some dynamical aspects of the action of automorphisms in model theory in particular in the presence of invariant measures. We give some characterizations for NIP theories in terms of dynamics of automorphisms and invariant measures…
Our purpose is to use a Darboux homogenous derivative to understand the harmonic maps with values in homogeneous space. We present a characterization of these harmonic maps from the geometry of homogeneous space. Furthermore, our work…
We study dynamical systems using measures taking values in a non-Archimedean field. The underlying space for such measure is a zero-dimensional topological space. In this paper we elaborate on the natural translation of several notions,…
The theory of polynomial-like maps is of fundamental importance in holomorphic dynamics. We study dynamical properties of a larger class of maps. Our main result is that, under some natural conditions, a map of this class has a completely…
We explore situations in which certain stochastic and high-dimensional deterministic systems behave effectively as low-dimensional dynamical systems. We define and study moment maps, maps on spaces of low-order moments of evolving…
Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…
We construct hierarchies of integrable systems invariant under the two-dimensional Darboux-Toda mapping for noncommuting objects, thus generalizing to the noncommutative case the integrable mapping approach to nonlinear dynamical systems.…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
We study expansive dynamical systems from the viewpoint of general topology. We introduce the notions of orbit and refinement expansivity on topological spaces extending expansivity in the compact metric setting. Examples are given on…
We give a brief survey on local holomorphic dynamics in higher dimensions. The main novelty of this note is that we will organize the material by the "level" of local invariants rather than the type of maps.
Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural…
We study random dynamical systems of certain continuous functions on the unit interval. We use bounded variation to provide sufficient conditions for unique ergodicity of these systems. Several classes of examples are provided.
We consider impulsive dynamical systems defined on compact metric spaces and their respective impulsive semiflows. We establish sufficient conditions for the existence of probability measures which are invariant by such impulsive semiflows.…
We consider hyperbolic projections of orbits of holomorphic self-maps of the unit disc, onto curves landing on the unit circle with a given angle. We show that under certain, necessary, assumptions, the projections exhibit monotonicity…
Motivated by non-equilibrium phenomena in nature, we study dynamical systems whose time-evolution is determined by non-stationary compositions of chaotic maps. The constituent maps are topologically transitive Anosov diffeomorphisms on a…
We study expanding circle maps interacting in a heterogeneous random network. Heterogeneity means that some nodes in the network are massively connected, while the remaining nodes are only poorly connected. We provide a probabilistic…
Understanding out-of-equilibrium quantum dynamics is a critical outstanding problem, with key questions regarding characterizing adiabaticity for applications in quantum technologies. We show how the metric-space approach to quantum…
We study the motion of independent particles in a dynamical random environment on the integer lattice. The environment has a product distribution. For the multidimensional case, we characterize the class of spatially ergodic invariant…