Related papers: Simultaneous Action of Finitely Many Interval Maps…
This paper establishes limit theorems for a class of stochastic hybrid systems (continuous deterministic dynamic coupled with jump Markov processes) in the fluid limit (small jumps at high frequency), thus extending known results for jump…
In a generic dynamical system chaos and regular motion coexist side by side, in different parts of the phase space. The border between these, where trajectories are neither unstable nor stable but of marginal stability, manifests itself…
We describe a general approach to the theory of self consistent transfer operators. These operators have been introduced as tools for the study of the statistical properties of a large number of all to all interacting dynamical systems…
The paper examines the discrete-time dynamics of neuron models (of excitatory and inhibitory types) with piecewise linear activation functions, which are connected in a network. The properties of a pair of neurons (one excitatory and the…
We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the…
This paper is concerned with statistical inference for infinite range interaction Gibbs point processes and in particular for the large class of Ruelle superstable and lower regular pairwise interaction models. We extend classical…
We study countably piecewise continuous, piecewise monotone interval maps. We establish a necessary and sufficient criterion for the existence of a nondecreasing semiconjugacy to a map of constant slope in terms of the existence of an…
We study sequences of partitions of a non decreasing sequence I n of intervals into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according…
We examine the long-run behavior of a wide range of dynamics for learning in nonatomic games, in both discrete and continuous time. The class of dynamics under consideration includes fictitious play and its regularized variants, the…
We study the momentum operator defined on the disjoint union of two intervals. Even in one dimension, the question of two non-empty open and non-overlapping intervals has not been worked out in a way that extends the cases of a single…
In a recent paper, we introduced the simultaneous representation problem (defined for any graph class C) and studied the problem for chordal, comparability and permutation graphs. For interval graphs, the problem is defined as follows. Two…
We study statistical properties of a family of maps acting in the space of integer valued sequences, which model dynamics of simple deterministic traffic flows. We obtain asymptotic (as time goes to infinity) properties of trajectories of…
Given a multimodal interval map $f:I \to I$ and a H\"older potential $\phi:I \to \mathbb{R}$, we study the dimension spectrum for equilibrium states of $\phi$. The main tool here is inducing schemes, used to overcome the presence of…
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 consider integer-valued random walks with independent but not identically distributed increments, and extend to this context several classical estimates, including a local limit theorem, precise small-ball estimates (both conditional on…
This paper summarizes the fundamental expressiveness, closure, and decidability properties of various finite-state automata classes with multiple input tapes. It also includes an original algorithm for the intersection of one-way…
Let $f$ be a piecewise continuous and monotonic map on the interval with at most finitely many discontinuities and turning points. In this paper we study properties about this class of maps and show its main difference from the continuous…
An interval graph has interval count $\ell$ if it has an interval model, where among every $\ell+1$ intervals there are two that have the same length. Maximum Cut on interval graphs has been found to be NP-complete recently by Adhikary et…
We give an example of a sequential dynamical system consisting of intermittent-type maps which exhibits loss of memory with a polynomial rate of decay. A uniform bound holds for the upper rate of memory loss. The maps may be chosen in any…
We study systems of globally coupled interval maps, where the identical individual maps have two expanding, fractional linear, onto branches, and where the coupling is introduced via a parameter - common to all individual maps - that…