Related papers: Different Statistical Behaviors of Orbits
We describe a topological mechanism for the existence of diffusing orbits in a dynamical system satisfying the following assumptions: (i) the phase space contains a normally hyperbolic invariant manifold diffeomorphic to a two-dimensional…
While studying gradient dynamical systems (DSs), Morse introduced the idea of encoding the qualitative behavior of a DS into a graph. Smale later refined Morse's idea and extended it to Axiom-A diffeomorphisms on manifolds. In Smale's…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
Dynamical systems having many coexisting attractors present interesting properties from both fundamental theoretical and modelling points of view. When such dynamics is under bounded random perturbations, the basins of attraction are no…
There are well-known examples of dynamical systems for which the Birkhoff averages with respect to a given observable along some or all of the orbits do not converge. It has been suggested that such orbits could be classified using higher…
The discovery of multi-planet extrasolar systems has kindled interest in using their orbital evolution as a probe of planet formation. Accurate descriptions of planetary orbits identify systems which could hide additional planets or be in a…
In this paper we study the dynamics of a general non-autonomous dynamical system generated by a family of continuous self maps on a compact space $X$. We derive necessary and sufficient conditions for the system to exhibit complex dynamical…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
Vertical thermal convection system exhibits weak turbulence and spatio-temporally chaotic behaviour. In this system, we report seven equilibria and 26 periodic orbits, all new and linearly unstable. These orbits, together with four…
Given a rational map of the Riemann sphere and a subset $A$ of its Julia set, we study the $A$-exceptional set, that is, the set of points whose orbit does not accumulate at $A$. We prove that if the topological entropy of $A$ is less than…
We study the set of irregular points for topologically mixing subshifts of finite type. It is well known that despite the irregular set having zero measure for every invariant measure, it has full topological entropy and full Hausdorff…
The horizontal dynamics of a bouncing ball interacting with an irregular surface is investigated and is found to demonstrate behavior analogous to a random walk. Its stochastic character is substantiated by the calculation of a permutation…
Three topics in dynamical systems are discussed. In the first two sections we solve some open problems concerning, respectively, Furstenberg entropy of stationary dynamical systems, and uniformly rigid actions admitting a weakly mixing…
We present a general mechanism to establish the existence of diffusing orbits in a large class of nearly integrable Hamiltonian systems. Our approach relies on successive applications of the `outer dynamics' along homoclinic orbits to a…
We study the behavior of orbits in two different galactic dynamical models, describing the motion in the central parts of a triaxial elliptical galaxy with a dense nucleus. Numerical experiments show that both models display regular motion…
Nonequilibrium statistical mechanics exhibit a variety of complex phenomena far from equilibrium. It inherits challenges of equilibrium, including accurately describing the joint distribution of a large number of configurations, and also…
The non-extensive statistical mechanics has been applied to describe a variety of complex systems with inherent correlations and feedback loops. Here we present a dynamical model based on previously proposed static model exhibiting in the…
This work introduces a new theoretical model for active matter ("complementary-spins" or c-spins), exploring the interplay of positional and orientational order in mobile agents with rotational freedom, divided into two populations with…
Tipping points are abrupt, drastic, and often irreversible changes in the evolution of non-stationary and chaotic dynamical systems. For instance, increased greenhouse gas concentrations are predicted to lead to drastic decreases in low…
Dynamists have been studying Hamiltonian systems for a long time. However, many physical systems are dissipative and do not preserve a symplectic form. This is the case, for example, with systems involving friction, which multiply the…