Related papers: Eigenvalues, K-theory and Minimal Flows

Let $\mathcal{C}$ be a class of graphs closed under taking induced subgraphs. We say that $\mathcal{C}$ has the {\em clique-stable set separation property} if there exists $c \in \mathbb{N}$ such that for every graph $G \in \mathcal{C}$…

We define oscillating sequences which include the M\"obius function in the number theory. We also define minimally mean attractable flows and minimally mean-L-stable flows. It is proved that all oscillating sequences are linearly disjoint…

Let G denote a compact connected Lie group with torsion-free fundamental group acting on a compact space X such that all the isotropy subgroups are connected subgroups of maximal rank. Let $T\subset G$ be a maximal torus with Weyl group W.…

The transposition graph $Cay(S_n,T_n)$ is the Cayley graph on the symmetric group $S_n$ generated by the set $T_n$ of all transpositions. In this paper, we show that each integer in the interval $\left[-{\lfloor(2n+1)/3 \rfloor\choose 2},…

We study basic properties of flow equivalence on one-dimensional compact metric spaces with a particular emphasis on isotopy in the group of (self-) flow equivalences on such a space. In particular, we show that an orbit-preserving such map…

Multiplicative relations in the cohomology ring of a manifold impose constraints upon its stable systoles. Given a compact Riemannian manifold (X,g), its real homology H_*(X,R) is naturally endowed with the stable norm. Briefly, if h\in…

Let $(X,G)$ be a minimal equicontinuous dynamical system, where $X$ is a compact metric space and $G$ some topological group acting on $X$. Under very mild assumptions, we show that the class of regular almost automorphic extensions of…

We study minimum degree conditions under which a graph $G$ contains $k$th powers of paths and cycles of arbitrary specified lengths. We determine precise thresholds, assuming that the order of $G$ is large. This extends a result of Allen,…

The embedded template is a geometric tool in dynamics being used to model knots and links as periodic orbits of $3$-dimensional flows. We prove that for an embedded template in $S^3$ with fixed homeomorphism type, its boundary as a…

Suppose $G$ is a compact Lie group, $H$ is a closed subgroup of $G$, and the homogeneous space $G/H$ is connected. The paper investigates the Ricci flow on a manifold $M$ diffeomorphic to $[0,1]\times G/H$. First, we prove a short-time…

A compact metric space $X$ and a discrete topological acting group $T$ give a flow $(X,T)$. Robert Ellis had initiated the study of dynamical properties of the flow $(X,T)$ via the algebraic properties of its "Enveloping Semigroup" $E(X)$.…

We study the dynamics of a family K_alpha of discontinuous interval maps whose (infinitely many) branches are Moebius transformations in SL(2, Z), and which arise as the critical-line case of the family of (a, b)-continued fractions. We…

Let $T\times X\rightarrow X, (t,x)\mapsto tx$, be a topological semiflow on a topological space $X$ with phase semigroup $T$. We introduce and discuss in this paper various transitivity dynamics of $(T,X)$.

We show that the characteristic polynomial and the Lefschetz zeta function are manifestations of the trace map from the $K$-theory of endomorphisms to topological restriction homology (TR). Along the way we generalize Lindenstrauss and…

We identify a strong stability condition on minimal submanifolds that implies uniqueness and dynamical stability properties. In particular, we prove a uniqueness theorem and a C^1 dynamical stability theorem of the mean curvature flow for…

We study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for…

We prove that the rank of the cohomology of a closed symplectic manifold with coefficients in a field of characteristic $p$ is smaller than the number of periodic orbits of any non-degenerate Hamiltonian flow. Following Floer, the proof…

We prove that the inclusion of map(X,Y) into map(K(X),K(Y)) is continuous, where K(X) is the space of non-empty compact subsets of X (also known as the hyperspace of compact subsets of X), and both spaces of maps are endowed with the…

Given an irrational rotation $T$ on $\M T$ we settle necessary and sufficient conditions on a step function $\phi$ and $t\in \M T$ for the existence of measurable solutions to the cohomogical equation $$\exp{(2i\pi\phi)}=\e{2i\pi t}f/f\rond…

In this article we characterize measure theoretical eigenvalues of Toeplitz Bratteli-Vershik minimal systems of finite topological rank which are not associated to a continuous eigenfunction. Several examples are provided to illustrate the…