Related papers: On self-similarities of ergodic flows

The chaotic flow of elastic fluids at low Reynolds number (Re) is typically distinguished into elasto-inertial and elastic turbulence (EIT/ET). However, the clear separation among these two turbulent regimes in parallel flows with a gradual…

In this paper we mainly study the dynamical complexity of Birkhoff ergodic average under the simultaneous observation of any number of continuous functions. These results can be as generalizations of [6,35] etc. to study Birkhorff ergodic…

For a non-exceptional oriented surface S let Q(S) be the moduli space of area one quadratic differentials. We show that there is a Borel subset E of Q(S) which is invariant under the Teichmueller flow F^t and of full measure for every…

Motivated by Gromov's geodesic flow problem on hyperbolic groups $G$, we develop in this paper an analog using random walks. This leads to a notion of a harmonic analog $\Theta$ of the Bowen-Margulis-Sullivan measure on $\partial^2 G$. We…

For a geodesic flow on a negatively curved Riemannian manifold $M$ and some subset $A\subset T^1M$, we study the limit $A$-exceptional set, that is the set of points whose $\omega$-limit do not intersect $A$. We show that if the topological…

By constructing a non-empty domain of discontinuity in a suitable homogeneous space, we prove that every torsion-free projective Anosov subgroup is the monodromy group of a locally homogeneous contact Axiom A dynamical system with a unique…

Let $\mathcal{H}$ be a stratum of translation surfaces with at least two singularities, let $m_{\mathcal{H}}$ denote the Masur-Veech measure on $\mathcal{H}$, and let $Z_0$ be a flow on $(\mathcal{H}, m_{\mathcal{H}})$ obtained by…

In this paper we introduce and explore the notion of rigidity group, associated with a collection of finitely many sequences, and show that this concept has many, somewhat surprising characterizations of algebraic, spectral, and unitary…

In this paper, we study the pointwise convergence of centain continuous-time polynomial ergodic averages. Our approach is based on the topological models of measurable flows. One of the main results of this paper is as follows: Let $a\in…

The multiplier representation of the generalized symmetry group of a quasiperiodic flow on the n-torus defines, for each subgroup of the multiplier group of the flow, a group invariant of the smooth conjugacy class of that flow. This group…

Let {\phi} be an automorphism on a connected Lie group G. Through several G-subgroups associated to the dynamics of {\phi} we analyze their topological entropy. Assume that G belongs to the class of finite semisimple center Lie groups which…

Given a tree $T$ and a group $\Ga$ of automorphisms of $T$, we study the markovian properties of the geodesic flow on the quotient by $\Ga$ of the space of geodesics of $T$. For instance, when $T$ is the Bruhat-Tits tree of a semi-simple…

Let $G/K$ be an orbit of the adjoint representation of a compact connected Lie group $G$, $\sigma$ be an involutive automorphism of $G$ and $\tilde G$ be the Lie group of fixed points of $\sigma$. We find a sufficient condition for the…

We prove that the Ricci flow g(t) starting at any metric on the euclidean space that is invariant by a transitive nilpotent Lie group N, can be obtained by solving an ODE for a curve of nilpotent Lie brackets. By using that this ODE is the…

Structurally stable (rough) flows on surfaces have only finitely many singularities and finitely many closed orbits, all of which are hyperbolic, and they have no trajectories joining saddle points. The violation of the last property leads…

We demonstrate that the necessary condition for $SO(N) \times SO(N)$ duality invariance manifests as a partial differential equation in two-dimensional scalar theories. This condition, expressed as a partial differential equation,…

We give two proofs to an old result of E. Salehi, showing that the Weyl subalgebra $\mathcal{W}$ of $\ell^\infty(\mathbb{Z})$ is a proper subalgebra of $\mathcal{D}$, the algebra of distal functions. We also show that the family…

We provide a method for formulating superintegrable magnetic geodesic flows on reductive homogeneous spaces $M=G/A$, with $G$ a compact semisimple Lie group and $A$ a closed subgroup of $G$. In the twisted cotangent bundle…

Let $Q$ be a compact, connected $n$-dimensional Riemannian manifold, and assume that the geodesic flow is toric integrable. If $n \neq 3$ is odd, or if $\pi_1(Q)$ is infinite, we show that the cosphere bundle of $Q$ is equivariantly…

Consider a topological dynamical system where the group is abelian and the topologies are locally compact and second-countable. Given an invariant measure for this system, we show that if its dynamical spectrum is contained in some Borel…