Related papers: Asymptotic geometry of non-mixing sequences
If X is a proper CAT(-1)-space and $\Gamma$ a non-elementary discrete group of isometries acting properly discontinuously on X, it is shown that the geodesic flow on the quotient space Y=X/$\Gamma$ is topologically mixing, provided that the…
Partial dynamical symmetry describes a situation in which some eigenstates have a symmetry which the quantum Hamiltonian does not share. This property is shown to have a classical analogue in which some tori in phase space are associated…
We discuss a link between graph theory and geometry that arises when considering graph dynamical systems with odd interactions. The equilibrium set in such systems is not a collection of isolated points, but rather a union of manifolds,…
We construct new families of direct serendipity and direct mixed finite elements on general planer convex polygons that are $H^1$ and $H(div)$ conforming, respectively, and possess optimal order of accuracy for any order. They have a…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
In this paper we study the dynamics of a general non-autonomous dynamical system generated by a family of continuous self maps on a compact space $X$. We derive necessary and sufficient conditions for the system to exhibit complex dynamical…
We discuss the noncommutative generalizations of polynomial algebras which after appropriate completions can be used as coordinate algebras in various noncommutative settings, (noncommutative differential geometry, noncommutative algebraic…
Discrete models have a long tradition in engineering, including finite state machines, Boolean networks, Petri nets, and agent-based models. Of particular importance is the question of how the model structure constrains its dynamics. This…
In the scope of the statistical description of dynamical systems, one of the defining features of chaos is the tendency of a system to lose memory of its initial conditions (more precisely, of the distribution of its initial conditions).…
This paper is the first part of a two-fold study of mixing, i.e. the formation of layers and upwelling of buoyancy, in axially stratified Taylor--Couette flow, with fixed outer cylinder. Using linear analysis and direct numerical…
We discuss the variety of coordinates often used to characterize the coherent state classical limit of an algebraic model. We show selection of appropriate coordinates naturally motivates a procedure to generate a single particle…
In this article we find explicit formulae for spherically symmetric solutions of the multidimensional zero-pressure gas dynamics system and its adhesion approximation. The asymptotic behaviour of the explicit solutions of the adhesion…
We approach the analysis of dynamical and geometrical properties of nonholonomic mechanical systems from the discussion of a more general class of auxiliary constrained Hamiltonian systems. The latter is constructed in a manner that it…
We complete the picture how the asymptotic behavior of a dynamical system is reflected by properties of the associated Perron-Frobenius operator. Our main result states that strong convergence of the powers of the Perron-Frobenius operator…
We study the 3-form flux $H_{\m\n\l}$ associated with the semi-classical geometry of $G/H$ gauged WZW models. We derive a simple, general expression for the flux in an orthonormal frame and use it to explicitly verify conformal invariance…
There are well-known analogs of the prime number theorem and Mertens' theorem for dynamical systems with hyperbolic behaviour. Here we consider the same question for the simplest non-hyperbolic algebraic systems. The asymptotic behaviour of…
We compute symmetry algebras of a system of two equations y^(k)=z^(l)=0, where 2<=k<l. It appears that there are many ways to convert such system of ODEs to an exterior differential system. They lead to different series of…
Mixing-via-shearing is a powerful and versatile method for establishing mixing properties of smooth parabolic flows. In its quantitative form, it provides upper bounds on the decay of correlations for sufficiently smooth observables.…
Active matter has played a pivotal role in advancing our understanding of non-equilibrium systems, leading to a fundamental shift in the study of biophysical phenomena. The foundation of active matter research is built on assumptions…
We introduce a geometric dynamical system where iteration is defined as a cycling composition of different maps acting on a space composed of three or more lines in $\mathbb{R}^2$. This system is motivated by the dynamics of iterated…