Related papers: Critical intermittency in random interval maps
Intermittent dynamics is characterized by long periods of different types of dynamical characteristics, for instance almost periodic dynamics alternated by chaotic dynamics. Critical intermittency is intermittent dynamics that can occur in…
Recently for a class of critically intermittent random systems a phase transition was found for the finiteness of the absolutely continuous invariant measure. The systems for which this result holds are characterized by the interplay…
For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending…
We consider a class of doubly intermittent maps with critical points, unbounded derivative and regularly varying tails. Under some mild assumptions we prove the existence of a unique mixing absolutely continuous invariant measure and give…
Using a renormalization method, we study the critical behavior for intermittency in two coupled one-dimensional (1D) maps. We find two fixed maps of the renormalization transformation. They all have common relevant eigenvalues associated…
The natural measure in a map with type-III intermittent chaos is used to define critical exponents for the average of a variable from a dynamical system near bifurcation. Numerical experiments were done with maps and verify the analytical…
On the basis of a lattice gas model and the convolution formula with cell construction scheme, we demonstrate that intermittency in the rapidity-space with respect to the scaled moments comes from a phase transition between ordered phase…
We consider a type of intermittent behavior that occurs as the result of the interplay between dynamical mechanisms giving rise to type-II intermittency and random dynamics. We analytically deduce the law for the distribution of the laminar…
We study the transitions to spatio-temporal intermittency in networks of randomly coupled Chate-Manneville maps. The relevant paprameters are the network connectivity, coupling strength, and the local parameter of the map. We show that the…
We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a…
We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely…
Intermittent large amplitude events are seen in the temporal evolution of a state variable of many dynamical systems. Such intermittent large events suddenly start appearing in dynamical systems at a critical value of a system parameter and…
We establish self-norming central limit theorems for non-stationary time series arising as observations on sequential maps possessing an indifferent fixed point. These transformations are obtained by perturbing the slope in the…
This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case…
We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in…
We construct a one-dimensional piecewise linear intermittent map from the interevent time distribution for a given renewal process. Then, we characterize intermittency by the asymptotic behavior near the indifferent fixed point in the…
We study random transformations built from intermittent maps on the unit interval that share a common neutral fixed point. We focus mainly on random selections of Pomeu-Manneville-type maps $T_\alpha$ using the full parameter range $0<…
The chaotic phenomenon of intermittency is modeled by a simple map of the unit interval, the Farey map. The long term dynamical behaviour of a point under iteration of the map is translated into a spin system via symbolic dynamics. Methods…
Stochastic dynamical systems consisting of non-invertible continuous maps on an interval are studied. It is proved that if they satisfy the recently introduced so-called $\mu$-injectivity and some mild assumptions, then proximality,…
We investigate indeterminate points in discrete integrable system. They appear in singularity confinement phenomenon naturally. We develop a method to analyse indeterminate points of dynamical maps and using this method we clarify behaviour…