Related papers: Measure Rigidity beyond Homogeneous Dynamics
We obtain a representation of an inhomogeneous Levy process in a Lie group or a homogeneous space in terms of a drift, a matrix function and a measure function. Because the stochastic continuity is not assumed, our result generalizes the…
In this paper we provide a detailed topological and measure-theoretic study of Lebesgue measure-preserving circle maps that are rotated with inner and outer rotations which are independent of each other. In particular, we analyze the…
Certain topological dynamical systems are considered that arise from actions of $\sigma$-compact locally compact Abelian groups on compact spaces of translation bounded measures. Such a measure dynamical system is shown to have pure point…
We investigate the homotopy type of a certain homogeneous space for a simple complex algebraic group. We calculate some of its classical topological invariants and introduce a new one. We also propose several conjectures about its…
We study actions by lattices in higher-rank (semi)simple Lie groups on compact manifolds. By classifying certain measures invariant under a related higher-rank abelian action (the diagonal action on the suspension space) we deduce a number…
We discuss some aspects of the extension to continuous systems of a statistical measure of complexity introduced by Lopez-Ruiz, Mancini and Calbet (LMC) [Phys. Lett. A 209 (1995) 321]. In general, the extension of a magnitude from the…
We propose a definition of magnitude for a length space with a Borel measure, which involves integrals over the set of geodesics. This quantity agrees with the magnitude of finite metric spaces, up to re-scaling the metric to ensure the…
Homodyne tomography provides a way for measuring generic field-operators. Here we analyze the determination of the most relevant quantities: intensity, field, amplitude and phase. We show that tomographic measurements are affected by…
In this paper, we establish a Liouville type rigidity result for a class of asymptotically hyperbolic non-compact Einstein metrics defined on manifolds of dimension $d\ge 5$ extending the earlier result in dimension $d=4$.
We study concentration of measure in Lie group actions. We define the notion of concentration locus of a flag sequence of Lie groups. Some examples of infinite group action on an infinite dimensional compact and non compact manifold show…
We investigate rigidity of measurable structure for higher rank abelian algebraic actions. In particular, we show that ergodic measures for these actions fiber over a 0 entropy measure with Haar measures along the leaves. We deduce various…
The (e,n)-complexity functions describe total instability of trajectories in dynamical systems. They reflect an ability of trajectories going through a Borel set to diverge on the distance $\epsilon$ during the time interval n. Behavior of…
Dynamic heterogeneity is now recognised as a central aspect of structural relaxation in disordered materials with slow dynamics, and was the focus of intense research in the last decade. Here we describe how initial, indirect observations…
Using methods from symplectic topology, we prove existence of invariant variational measures associated to the flow $\phi_H$ of a Hamiltonian $H\in C^{\infty}(M)$ on a symplectic manifold $(M,\omega)$. These measures coincide with Mather…
An attempt is made to extend some of the basic paradigms of dynamics, from the viewpoint of (continuous) flows, to non-metric manifolds.
The title refers to the area of research which studies infinite groups using measure-theoretic tools, and studies the restrictions that group structure imposes on ergodic theory of their actions. The paper is a survey of recent developments…
In the realm of Delone sets in locally compact, second countable, Hausdorff groups, we develop a dynamical systems approach in order to study the continuity behavior of measured quantities arising from point sets. A special focus is both on…
A topological commutative ring is said to be rigid when for every set $X$, the topological dual of the $X$-fold topological product of the ring is isomorphic to the free module over $X$. Examples are fields with a ring topology, discrete…
We give simple and unified proofs of the known stability and rigidity results for Lie algebras, Lie subalgebras and Lie algebra homomorphisms. Moreover, we investigate when a Lie algebra homomorphism is stable under all automorphisms of the…
Empirical researchers often use slope-homogeneity tests to assess whether slopes can be treated as common across units. A key difficulty is that heterogeneity may be concentrated in a small number of units, so that a failure to reject…