Related papers: Symbolic extensions and uniform generators for top…
We provide a survey of results from symbolic dynamics and algebraic topology relating to Grout, a new user-friendly program developed to calculate combinatorial properties and topological invariants of a large class of symbolic…
A continuous cohomology theory for topological quandles is introduced, and compared to the algebraic theories. Extensions of topological quandles are studied with respect to continuous 2-cocycles, and used to show the differences in second…
The aim of this paper is to obtain an asymptotic expansion for ergodic integrals of translation flows on flat surfaces of higher genus (Theorem 1) and to give a limit theorem for these flows (Theorem 2).
Caroline Series' [{\em The modular surface and continued fractions}, J. Lond. Math. Soc. (2), {\bf 31}, no.~1, (1985), 69--80] gives a clear framework linking, in a deceptively simple way, the dynamics of the geodesic flow on the modular…
We introduce the notions of topological entropy of a formal language and of a topological automaton. We show that the entropy function is surjective and bound the entropy of languages accepted by deterministic {\epsilon}-free push-down…
Periodically driven flows are fundamental models of chaotic behavior and the study of their transport properties is an active area of research. A well-known analytic construction is the augmentation of phase space with an additional time…
We present an overview of some recent developments in the theory of generalized formal series, grounded in diffeological geometric framework. These constructions aim to offer new tools for understanding infinite-dimensional phenomena in…
We introduce and prove basic results about several graph-theoretic notions relevant to the multiresolution analysis of flow graphs that represent the transfer of control in computer programs. We take a category-theoretical viewpoint to…
Let $X\in\mathbb{R}^{n}$ or $\mathbb{C}^{n}$. For $\phi:\mathbb{R}^{n}\mapsto\mathbb{R}^{n}$ (respectively, $\phi:\mathbb{C}^{n}\mapsto\mathbb{C}^{n}$) and $t\in\mathbb{R}$ (respectively, $\mathbb{C}$), we put $\phi^{t}=t^{-1}\phi(Xt)$. A…
Let $X$ be a compact metric space and $\Phi=\{\varphi_t\}_{t\in\mathbb{R}}$ be a continuous flow on $X$. We introduce two types of topological pressure for family of discontinuous potentials $a=\{a_t\}_{t>0}$. First, define the topological…
This paper clarifies a global structure of Stokes-Dirac structures used for describing interconnected port-Hamiltonian systems defined on manifolds with non-trivial topology under consistent boundary condition.
Graphs are a basic tool for the representation of modern data. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological…
In this paper we investigate some connections between Topological Dynamics, the theory of G-Principal Bundles, and the theory of Locally Trivial Groupoids.
We show that every partially hyperbolic diffeomorphism with a 1-dimensional center bundle has a principal symbolic extension. On the other hand, we show there are no symbolic extensions $C^1$-generically among diffeomorphisms containing…
For real application and theoretical investigation of ordinary hypergraphs and non-ordinary hypergraphs, researchers need to establish standard rules and feasible operating methods. We propose a visualization tool for investigating…
We introduce the notion of induced topological pressure for countable state Markov shifts with respect to a non-negative scaling function and an arbitrary subset of finite words. Firstly, the scaling function allows a direct access to…
This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order…
We show that for every non-elementary hyperbolic group, an associated topological flow space admits a coding based on a transitive subshift of finite type. Applications include regularity results for Manhattan curves, the uniqueness of…
Final version. To appear in Discrete and Continuous Dynamical Systems - A.
The aim of this paper is to obtain an asymptotic expansion for ergodic integrals of translation flows on flat surfaces of higher genus (Theorem 1) and to give a limit theorem for these flows (Theorem 2).