Related papers: Newhouse phenomena in the Fibonacci trace map
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on the dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures…
It is known that the famous Feigenbaum-Coullet-Tresser period doubling universality has a counterpart for area-preserving maps of ${\fR}^2$. A renormalization approach has been used in \cite{EKW1} and \cite{EKW2} in a computer-assisted…
Considering random noise in finite dimensional parameterized families of diffeomorphisms of a compact finite dimensional boundaryless manifold M, we show the existence of time averages for almost every orbit of each point of M, imposing…
We study the problem of persistence of attractors with smooth boundary for a class of set-valued dynamical systems that naturally arise in the context of random and control dynamical systems, as well as in systems modeling the dynamical…
In this paper, we consider chaotic dynamics and variational structures of area-preserving maps. There is a lot of study on dynamics of their maps and the works of Poincare and Birkhoff are well-known. To consider variational structures of…
Recently, there has been an increasing interest on nonautonomous composition of perturbed hyperbolic systems: composing perturbations of a given hyperbolic map $F$ results in statistical behaviour close to that of $F$. We show this fact in…
We consider the spectrum of the Fibonacci Hamiltonian for small values of the coupling constant. It is known that this set is a Cantor set of zero Lebesgue measure. Here we study the limit, as the value of the coupling constant approaches…
We study two classes of dynamical systems with holes: expanding maps of the interval and Collet-Eckmann maps with singularities. In both cases, we prove that there is a natural absolutely continuous conditionally invariant measure $\mu$…
A nearly-integrable dynamical system has a natural formulation in terms of actions, $y$ (nearly constant), and angles, $x$ (nearly rigidly rotating with frequency $\Omega(y)$). We study angle-action maps that are close to symplectic and…
We consider order preserving $C^3$ circle maps with a flat piece, Fibonacci rotation number, critical exponents $(\ell_1, \ell_2)$ and negative shwarzian derivative. This paper treat the geometry characteristic of the non-wondering (cantor…
We present a one-parameter family of continuous, piecewise affine, area preserving maps of the square, which are inspired by a dynamical system in game theory. Interested in the coexistence of stochastic and (quasi-)periodic behaviour, we…
In this note, we use a toy problem of detecting cycles of length two in a tent map to highlight some curious phenomena in the behavior of discrete dynamical systems. This work presents no new results or proofs, only computer experiments and…
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…
In this paper, the mathematical framework providing a description of completely positive and trace preserving dynamics of open quantum systems is addressed. Special case of time-dependent Lindbladian governed by periodic Hamiltonian is…
In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…
Structures such as waves, jets, and vortices have a dramatic impact on the transport properties of a flow. Passive tracer transport in incompressible two-dimensional flows is described by Hamiltonian dynamics, and, for idealized structures,…
For a class of flows on polytopes, including many examples from Evolutionary Game Theory, we describe a piecewise linear model which encapsulates the asymptotic dynamics along the heteroclinic network formed out of the polytope's vertexes…
We study the ergodic properties of generic continuous dynamical systems on compact manifolds. As a main result we prove that generic homeomorphisms have convergent Birkhoff averages under continuous observables at Lebesgue almost every…
We study a class of homeomorphisms of surfaces collectively known as linked-twist maps. We introduce an abstract definition which enables us to give a precise characterisation of a property observed by other authors, namely that such maps…