Related papers: Rank one and mixing differentiable flows

We give a condition on a piecewise constant roof function and an irrational rotation by $\alpha$ on the circle to give rise to a special flow having the mild mixing property. Such flows will also satisfy Ratner's property. As a consequence…

We study discrete flow equivalence of two-sided topological Markov shifts by using extended Ruelle algebras. We characterize flow equivalence of two-sided topological Markov shifts in terms of conjugacy of certain actions weighted by…

We establish necessary and sufficient conditions for suspension flows over certain families of shift spaces to be topologically mixing. We also show the similarities and differences between this case and the smooth measure theoretic setting…

In this paper, we study topological properties of the right action by translation of the Weyl Chamber flow on the space of Weyl chambers. We obtain a necessary and sufficient condition for topological mixing. (1)

We performed a numerical study of the efficiency of mixing by alternating horizontal and vertical shear ``wedge'' flows on the two-dimensional torus. Our results suggest that except in cases where each individual flow is applied for only a…

For flows the rank is an invariant by linear change of time. But what we can say about isomorphisms? It seems that in case of mixing flows this problem is the most difficult. However the known technique of joinings provides non-isomorphism…

Let $T=(T_t^f)_{t\in \mathbb{R}}$ be a special flow built over an IET $T : T \to T$ of bounded type, under a roof function f with symmetric logarithmic singularities at a subset of discontinuities of T. We show that $T$ satisfies so-called…

Let $Y$ be a topological Markov chain with finite leading and follower sets. Special flow over $Y$ whose height function depends on the time zero of elements of $Y$ is constructed. Then a formula for computing the entropy of this flow will…

We prove mixing on a general class of rank-one transformations containing all known examples of rank-one mixing, including staircase transformations and Ornstein's constructions, and a variety of new constructions.

We consider suspension flows built over interval exchange transformations with the help of roof functions having an asymmetric logarithmic singularity. We prove that such flows are strongly mixing for a full measure set of interval exchange…

We give a geometric criterion that guaranteesa purely singular spectral type for a dynamical system on a Riemannian manifold. The criterion, that is based on the existence of fairly rich but localized periodic approximations, is compatible…

The liftable centralizer for special flows over irrational rotations is studied. It is shown that there are such flows under piecewise constant roof functions which are rigid and whose liftable centralizer is trivial.

We consider special flows over two-dimensional rotations by $(\alpha,\beta)$ on $\T^2$ and under piecewise $C^2$ roof functions $f$ satisfying von Neumann's condition $\int_{\T^2}f_x(x,y)\,dx\,dy\neq 0\neq \int_{\T^2}f_y(x,y)\,dx\,dy.$ Such…

This paper introduces the notions of vector field and flow on a general differentiable stack. Our main theorem states that the flow of a vector field on a compact proper differentiable stack exists and is unique up to a uniquely determined…

Arnol'd and Kochergin mixing conservative flows on surfaces stand as the main and almost only natural class of mixing transformations for which higher order mixing has not been established, nor disproved. Under suitable arithmetic…

The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterised by swirls, jets, and topological disclinations in their orientation field. However, the ability to…

We provide sufficient conditions on a positive function so that its associated special flow over any irrational rotation is either weak mixing or $L^2$-conjugate to a suspension flow.

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…

We show that solutions to certain higher-order intrinsic geometric flows on a compact manifold, including some flows generated by the ambient obstruction tensor, are unique. With the goal of providing a complete self-contained proof,…

We describe all possible topological structures of Morse flows and typical gradient saddle-nod bifurcation of flows on the 2-dimensional torus with a hole in the case that the number of singular point of flows is at most six. To describe…