Dynamical systems and Lagrangian spaces.
Dynamical systems and shapes.
This survey is an introduction to some of the methods, techniques and concepts from algebraic topology and related areas (homotopy theory, shape theory) which can be fruitfully applied to study problems concerning continuous dynamical systems. To this end two instances which exemplify the interaction between topology and dynamics are considered, namely, Conley’s index theory and the study of some properties of certain attractors.
Dynamical systems and the homology norm of a 3-manifold II.
Dynamical systems arising from elliptic curves
We exhibit a family of dynamical systems arising from rational points on elliptic curves in an attempt to mimic the familiar toral automorphisms. At the non-archimedean primes, a continuous map is constructed on the local elliptic curve whose topological entropy is given by the local canonical height. Also, a precise formula for the periodic points is given. There follows a discussion of how these local results may be glued together to give a map on the adelic curve. We are able to give a map whose...
Dynamical systems on Riemannian manifolds. (Systèmes dynamiques sur des espaces de Riemann.)
Dynamical systems on vector bundles.
Dynamical systems -- past and present.
Dynamical systems with multiplicative perturbations: the strong convergence of measures
We give sufficient conditions for the strong asymptotic stability of the distributions of dynamical systems with multiplicative perturbations. We apply our results to iterated function systems.
Dynamical systems with Newtonian type potentials
We study the existence of regular periodic solutions to some dynamical systems whose potential energy is negative, has only a singular point and goes to zero at iniìnity. We give sufficient conditions to the existence of periodic solutions of assigned period which do not meet the singularity.
Dynamical zeta functions and Kummer congruences
Dynamical zeta functions, congruences in Nielsen theory and Reidemeister torsion
In this paper we prove trace formulas for the Reidemeister numbers of group endomorphisms and the rationality of the Reidemeister zeta function in the following cases: the group is finitely generated and the endomorphism is eventually commutative; the group is finite; the group is a direct sum of a finite group and a finitely generated free Abelian group; the group is finitely generated, nilpotent and torsion free. We connect the Reidemeister zeta function of an endomorphism of a direct sum of a...
Dynamically defined Cantor sets under the conditions of McDuff's conjecture
We prove that if the Cantor set K, dynamically defined by a function , satisfies the conditions of McDuff’s conjecture then it cannot be C¹-minimal.
Dynamické systémy s regulární pravou stranou. I
Dynamické systémy s regulární pravou stranou. II
Dynamics in binary neural networks with a finite number of patterns. I: General picture of the asynchronous zero temperature dynamics.
Dynamics in the moduli space of Abelian differentials.
Dynamics of a certain sequence of powers.
Dynamics of a Lotka-Volterra map
Given the plane triangle with vertices (0,0), (0,4) and (4,0) and the transformation F: (x,y) ↦ (x(4-x-y),xy) introduced by A. N. Sharkovskiĭ, we prove the existence of the following objects: a unique invariant curve of spiral type, a periodic trajectory of period 4 (given explicitly) and a periodic trajectory of period 5 (described approximately). Also, we give a decomposition of the triangle which helps to understand the global dynamics of this discrete system which is linked with the behavior...
Dynamics of a nonautonomous Leslie-Gower type food chain model with delays.
Dynamics of a predator-prey system concerning biological and chemical controls.