Related papers: Critical intermittency in rational maps
There exists a variety of physically interesting situations described by continuous maps that are nondifferentiable on some surface in phase space. Such systems exhibit novel types of bifurcations in which multiple coexisting attractors can…
Universal critical properties can manifest themselves not only in spatial but also in temporal directions. It has been found that critical point with emergent symmetry exhibits intriguing spatial critical properties characterized by two…
We analyze a one-dimensional piecewise continuous discrete model proposed originally in studies on population ecology. The map is composed of a linear part and a power-law decreasing piece, and has three parameters. The system presents both…
This paper is part of a program to understand the parameter spaces of dynamical systems generated by meromorphic functions with finitely many singular values. We give a full description of the parameter space for a specific family based on…
As a particular problem within the field of non-autonomous discrete systems, we consider iterations of two quadratic maps $f_{c_0}=z^2+c_0$ and $f_{c_1}=z^2+c_1$, according to a prescribed binary sequence, which we call a \emph{template}.…
We consider $(1,2)$-rational functions given on the field of $p$-adic numbers $\mathbb Q_p$. In general, such a function has four parameters. We study the case when such a function has two fixed points and show that when there are two fixed…
In type I intermittency, simple models known for at least twenty years show that a characteristic u-shaped probability distribution is obtained for the laminar phase length. We have shown elsewhere that, for some cases of pathology, the…
For polynomials and rational maps of fixed degree over a finite field, we bound both the average number of connected components of their functional graphs as well as the average number of periodic points of their associated dynamical…
The ideas of dynamical complexity induced intermittent turbulence by sporadic localized interactions of coherent structures are discussed. In particular, we address the phenomenon of magnetic reconfiguration due to coarse-grained…
We study circle maps with a flat interval where the critical exponents at the two boundary points of the flat spot might be different. The space of such systems is partitioned in two connected parts whose common boundary only depends on the…
We analyze a pair of delay-coupled FitzHugh-Nagumo oscillators exhibiting in-out intermittency as a part of the generating mechanism of extreme events. We study in detail the characteristics of in-out intermittency and identify the…
Chaotic dynamics can be quite heterogeneous in the sense that in some regions the dynamics are unstable in more directions than in other regions. When trajectories wander between these regions, the dynamics is complicated. We say a chaotic…
In this paper we study quantitative recurrence and the shrinking target problem for dynamical systems coming from overlapping iterated function systems. Such iterated function systems have the important property that a point often has…
We describe a fundamental domain for the punctured Riemann surface $V_{3,m}$ which parametrises (up to M\"obius conjugacy) the set of quadratic rational maps with numbered critical points, such that the first critical point has period…
This paper presents a more complete version than hitherto published of our explanation of a transition from regular to irregular motions and more generally of the nature of a certain kind of deterministic chaos. To this end we introduced a…
The scope of the paper is the theoretical analysis of the time rate in which a dynamical system reaches a stable stationary state or stable oscillations. The method used for the analysis is based on the so-called iterative time profiles,…
We prove several generic existence results for infinitely many periodic orbits of Hamiltonian diffeomorphisms or Reeb flows. For instance, we show that a Hamiltonian diffeomorphism of a complex projective space or Grassmannian generically…
This paper establishes the theoretical foundation for statistical applications of an intriguing new type of spatial point processes called critical point processes. These point processes, residing in Euclidean space, consist of the critical…
Intermittent high-amplitude structures emerge in a damped and driven discrete nonlinear Schroedinger equation whose solutions transport both energy and particles from sources to sinks. These coherent structures are necessary for any…
The existing periodic orbit theory of spectral correlations for classically chaotic systems relies on the Riemann-Siegel-like representation of the spectral determinants which is still largely hypothetical. We suggest a simpler derivation…