Related papers: On multi-transitivity with respect to a vector
A graph is said to be edge-transitive if its automorphism group acts transitively on its edges. It is known that edge-transitive graphs are either vertex-transitive or bipartite. In this paper we present a complete classification of all…
We consider dynamical systems arising from substitutions over a finite alphabet. We prove that such a system is linearly repetitive if and only if it is minimal. Based on this characterization we extend various results from primitive…
Aldous [1] asked whether every graph in which the distribution of the return time of random is independent of the starting vertex must be transitive. We remark that this question can be reduced into a purely graph-theoretic one that had…
This paper considers the egodicity properties in iterated function systems. First, we will introduce chain mixing and chain transitive iterated function systems then some results and examples are presented to compare with these notions in…
This paper presents causal block-diagram models to represent the equations of motion of multi-body systems in a very compact and simple closed form. Both the forward dynamics (from the forces and torques imposed at the various…
In this paper we study some dynamical properties such as Frequent Hypercyclicity Criterion, chaos, disjoint hypercyclicity and F-transitivity via Furstenberg family F for generalized bilateral weighted shift operator on the standard Hilbert…
Recently, G\'{o}rska, Lema\'{n}czyk, and de la Rue characterized the class of automorphisms disjoint from all ergodic automorphisms. Inspired by their work, we provide several characterizations of systems that are disjoint from all minimal…
Recent evidence suggests that physiological signals under healthy conditions may have a fractal temporal structure. We investigate the possibility that time series generated by certain physiological control systems may be members of a…
Nonlinear dynamical systems subjected to a combination of noise and time-varying forcing can exhibit sudden changes, critical transitions or tipping points where large or rapid dynamic effects arise from changes in a parameter that are…
The architectures of multiple planet systems can provide valuable constraints on models of planet formation, including orbital migration, and excitation of orbital eccentricities and inclinations. NASA's Kepler mission has identified 1235…
The main aim of this paper is extending the concept of scambled pair and Li--Yorke chaos to non--uniform compact dynamical systems. We show for finite (compact Alexandroff) topological space $X$ with at least two elements the following…
We study shadowing-type properties for set-valued dynamical systems. In particular, we investigate the periodic shadowing property and its relationship with expansivity and chain transitivity. We establish that for positively expansive…
We investigate the spectral and transport properties of many-body quantum systems with conserved charges and kinetic constraints. Using random unitary circuits, we compute ensemble-averaged spectral form factors and linear-response…
Let $\phi:X\to \mathbb R$ be a continuous potential associated with a symbolic dynamical system $T:X\to X$ over a finite alphabet. Introducing a parameter $\beta>0$ (interpreted as the inverse temperature) we study the regularity of the…
A (closed) dynamical system is a notion of how things can be, together with a notion of how they may change given how they are. The idea and mathematics of closed dynamical systems has proven incredibly useful in those sciences that can…
Comparing with traditional fixed formation for a group of dynamical systems, time-varying formation can produce the following benefits: i) covering the greater part of complex environments; ii) collision avoidance. This paper studies the…
Information does not generally behave like a conservative fluid flow in communication networks with multiple sources and sinks. However, it is often conceptually and practically useful to be able to associate separate data streams with each…
Recurrence properties of systems and associated sets of integers that suffice for recurrence are classical objects in topological dynamics. We describe relations between recurrence in different sorts of systems, study ways to formulate…
Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations to component species' abundances without suffering adverse…
The present work is concerned with the eqiucontinuity and sensitivity of iterated function systems (IFSs). Here, we consider more general case of IFSs, i.e. the IFSs generated by a family of relations. We generalize the concepts of…