Related papers: Chaotic polynomial maps
Intermittent switchings between weakly chaotic (laminar) and strongly chaotic (bursty) states are often observed in systems with high-dimensional chaotic attractors, such as fluid turbulence. They differ from the intermittency of a…
For a certain parametrized family of maps on the circle with critical points and logarithmic singularities where derivatives blow up to infinity, we construct a positive measure set of parameters corresponding to maps which exhibit…
Examples of one-dimensional lattice systems are considered, in which patterns of different spatial scales arise alternately, so that the spatial phase over a full cycle undergo transformation according to expanding circle map that implies…
Self-consistent chaotic transport is studied in a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in…
Transition from quasiperiodicity with many frequencies (i.e., a high-dimensional torus) to chaos is studied by using $N$-dimensional globally coupled circle maps. First, the existence of $N$-dimensional tori with $N\geq 2$ is confirmed…
Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their…
In holomorphic dynamics, complex box mappings arise as first return maps to well-chosen domains. They are a generalization of polynomial-like mapping, where the domain of the return map can have infinitely many components. They turned out…
For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here ``eigenvalue''…
We point out the joint occurrence of Pascal triangle patterns and power-law scaling in the standard logistic map, or more generally, in unimodal maps. It is known that these features are present in its two types of bifurcation cascades:…
We examine a model system where attractors may consist of a heteroclinic cycle between chaotic sets; this `cycling chaos' manifests itself as trajectories that spend increasingly long periods lingering near chaotic invariant sets…
We give conditions under which nonuniformly expanding maps exhibit lower bounds of polynomial type for the decay of correlations and for a large class of observables. We show that if the Lasota-Yorke type inequality for the transfer…
Chaotic attractors in the two-dimensional border-collision normal form (a piecewise-linear map) can persist throughout open regions of parameter space. Such robust chaos has been established rigorously in some parameter regimes. Here we…
We introduce an interesting hierarchy of rational order chaotic maps that posses an invariant measure. In contrast to the previously introduced hierarchy of chaotic maps \cite{J1,J2,J3,J4,J5}, with merely entropy production, the rational…
Noise-induced phenomena in high-dimensional dynamical systems were investigated from a random dynamical systems point of view. In a class of generalized H\'enon maps, which are randomly perturbed delayed logistic maps, with monotonically…
We consider a linear-quadratic deterministic optimal control problem where the control takes values in a two-dimensional simplex. The phase portrait of the optimal synthesis contains second-order singular extremals and exhibits modes of…
We study the dynamics of the H\'enon map defined over complete, locally compact non-Archimedean fields of odd residue characteristic. We establish basic properties of its one-sided and two-sided filled Julia sets, and we determine, for each…
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…
The purpose of this paper is to initiate a theory concerning the dynamics of asymptotically holomorphic polynomial-like maps. Our maps arise naturally as deep renormalizations of asymptotically holomorphic extensions of $C^r$ ($r>3$)…
We consider each of the three classes of representations of cyclic groups that arise in the study of rational sphere maps. We study the possible number of terms for invariant polynomials with non-negative coefficients that are constant on…
We report in this paper a complete analytical study on the bifurcations and chaotic phenomena observed in certain second-order, non-autonomous, dissipative chaotic systems. One-parameter bifurcation diagrams obtained from the analytical…