Related papers: Non-autonomous dynamics of holomorphic mappings in…
In theoretical ecology, models describing the spatial dispersal and the temporal evolution of species having non-overlapping generations are often based on integrodifference equations. For various such applications the environment has an…
We present some constructions that are merely the fruit of combining recent results from two areas of smooth dynamics: nonuniformly hyperbolic systems and elliptic constructions.
We approach the analysis of dynamical and geometrical properties of nonholonomic mechanical systems from the discussion of a more general class of auxiliary constrained Hamiltonian systems. The latter is constructed in a manner that it…
The exact order of mixing for zero-dimensional algebraic dynamical systems is not entirely understood. Here non-Archimedean norms in function fields of positive characteristic are used to exhibit an asymptotic shape in non-mixing sequences…
For a commutative non-autonomous dynamical system we show that topological transitivity of the non-autonomous system induced on probability measures (hyperspaces) is equivalent to the weak mixing of the induced systems. Several counter…
We continue our study of the dynamics of mappings with small topological degree on (projective) complex surfaces. Previously, under mild hypotheses, we have constructed an ergodic ``equilibrium'' measure for each such mapping. Here we study…
We study the ergodicity of non-autonomous discrete dynamical systems with non-uniform expansion. As an application we get that any uniformly expanding finitely generated semigroup action of $C^{1+\alpha}$ local diffeomorphisms of a compact…
We investigate qualitative properties of positive singular solutions of some elliptic systems in bounded and unbounded domains. We deduce symmetry and monotonicity properties via the moving plane procedure. Moreover, in the unbounded case,…
Monomial mappings, $x\mapsto x^n$, are topologically transitive and ergodic with respect to Haar measure on the unit circle in the complex plane. In this paper we obtain an anologous result for monomial dynamical systems over $p-$adic…
Discussed is mechanics of objects with internal degrees of freedom in generally non-Euclidean spaces. Geometric peculiarities of the model are investigated detailly. Discussed are also possible mechanical applications, e.g., in dynamics of…
Geometrization of dynamics consists of representing trajectories by geodesics on a configuration space with a suitably defined metric. Previously, efforts were made to show that the analysis of dynamical stability can also be carried out…
This paper investigates a family of dynamical systems arising from an evolutionary re-interpretation of certain optimal control and optimization problems. We focus particularly on the application in image registration of the theory of…
In this paper, we seek to understand the behavior of dynamical systems that are perturbed by a parameter that changes discretely in time. If we impose certain conditions, we can study certain embedded systems within a hybrid system as…
We study ergodic properties of compositions of holomorphic endomorphisms of the complex projective space chosen independently at random according to some probability distribution. Along the way, we construct positive closed currents which…
Invariant manifolds are the skeleton of the chaotic dynamics in Hamiltonian systems. In Celestial Mechanics, for instance, these geometrical structures are applied to a multitude of physical and practical problems, such as to the…
When a granular system is tapped, its volume changes. Here, using a well-defined macroscopic protocol, we prepare an ensemble of granular systems and track the statistics of volume changes as a function of the number of taps. This is in…
Two types of dynamics, chaotic and monotone, are compared. It is shown that monotone maps in strongly ordered spaces do not have chaotic attracting sets.
The cosmological dynamics are rigorously investigated through the systematic application of autonomous system analysis to the gravitational field equations in non-metricity gravity. The systematic procedure to analyze the late-time cosmic…
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…
We initiate the study of random iteration of automorphisms of real and complex projective surfaces, or more generally compact K{\"a}hler surfaces, focusing on the fundamental problem of classification of stationary measures. We show that,…