Related papers: Embedding theorems for discrete dynamical systems …
In this work we study the problem of positiveness of topological entropy for flows using pointwise dynamics. We show that the existence of a non-periodic nonwandering point of an expansive and non-singular flow with shadowing is a…
We study two variations of Bowen's definitions of topological entropy based on separated and spanning sets which can be applied to the study of discontinuous semiflows on compact metric spaces. We prove that these definitions reduce to…
This series explores a new notion of T-homotopy equivalence of flows. The new definition involves embeddings of finite bounded posets preserving the bottom and the top elements and the associated cofibrations of flows. In this fourth part,…
For certain families of fluid flow, a new conserved quantity -- stream-helicity -- has been established.Using examples of linked and knotted streamtubes, it has been shown that stream-helicity does, in certain cases, entertain itself with a…
We derive a rigorous classification of topologically stable Fermi surfaces of non-interacting, discrete translation-invariant systems from electronic band theory, adiabatic evolution and their topological interpretations. For systems on an…
We characterize, using commuting zero-flux homologies, those volume-preserving vector fields on a $3$-manifold that are steady solutions of the Euler equations for some Riemannian metric. This result extends Sullivan's homological…
The embedding theorem arises in several problems from analysis and geometry. The purpose of this paper is to provide a deeper understanding of analysis and geometry with a particular focus on embedding theorems on spaces of homogeneous type…
We prove the upper semicontinuity of the measure theoretic entropy for the geodesic flow on complete Riemannian manifolds without focal points and bounded sectional curvature. We then study the relationship between the escape of mass…
Embedding static graphs in low-dimensional vector spaces plays a key role in network analytics and inference, supporting applications like node classification, link prediction, and graph visualization. However, many real-world networks…
We analyze the action of the spectral flows on N=2 twisted topological theories. We show that they provide a useful mapping between the two twisted topological theories associated to a given N=2 superconformal theory. This mapping can also…
Final version. To appear in Discrete and Continuous Dynamical Systems - A.
In analogy to the topological entropy for continuous endomorphisms of totally disconnected locally compact groups, we introduce a notion of topological entropy for continuous endomorphisms of locally linearly compact vector spaces. We study…
Takens' Embedding Theorem remarkably established that concatenating M previous outputs of a dynamical system into a vector (called a delay coordinate map) can be a one-to-one mapping of a low-dimensional attractor from the system state…
We relate stability properties (i.e. moment exponents) of a stochastic dynamical system on a compact manifold $M$ to the homotopy and integral homology groups of $M$. In the special case of gradient Brownian systems associated to isometric…
In this work we establish that finite directed graphs give rise to semiflows on the power set of their nodes. We analyze the topological dynamics for semiflows on finite directed graphs by characterizing Morse decompositions, recurrence…
We study semi-dynamical systems associated to delay differential equations. We give a simple criteria to obtain weak and strong persistence and provide sufficient conditions to guarantee uniform persistence. Moreover, we show the existence…
This study proposes a novel topology optimization method for unsteady fluid flows induced by actively moving rigid bodies. The key idea of the proposed method is to decouple the design and analysis domains by using separate grids. The…
The coupled in-plane diffusion dynamics between point-particles embedded in stacked fluid membranes are investigated. We calculate the contributions to the coupling longitudinal and transverse diffusion coefficients due to particle motion…
This paper develops a fixed-point iteration to solve the steady-state water flow equations in an urban water distribution network. The fixed-point iteration is derived upon the assumption of turbulent flow solutions and the validity of the…
We explore some properties of flows with strongly adapted 1-forms, originally discovered in (Tao 2017), which can be used to embed Turing machines into dynamical systems. In particular, we discuss some relations to geodesible flows, and…