Related papers: Definable Topological Dynamics of $SL_2(\mathbb{C}…

In this work, we prove that every SFT, sofic shift, and strongly irreducible shift on locally finite groups has strong dynamical properties. These properties include that every sofic shift is an SFT, every SFT is strongly irreducible, every…

The gradient flow bears a close resemblance to the coarse graining, the guiding principle of the renormalization group (RG). In the case of scalar field theory, a precise connection has been made between the gradient flow and the RG flow of…

We consider the topological dynamics of the automorphism group of a particular sparse graph M_1 resulting from an ab initio Hrushovski construction. We show that minimal subflows of the flow of linear orders on M_1 have all orbits meagre,…

Let $G$ be a finitely generated amenable group. We study the space of shifts on $G$ over a given finite alphabet $A$. We show that the zero entropy shifts are generic in this space, and that more generally the shifts of entropy $c$ are…

We develop a general strategy for constructing the explicit Local Langlands Correspondences for $p$-adic reductive groups via reduction to LLC for supercuspidal representations of proper Levi subgroups, using Hecke algebra techniques. As an…

We establish exponential decay of correlations of all orders for locally $G$-accessible isometric extensions of transitive Anosov flows, under the assumption that the strong stable and strong unstable foliations of the base Anosov flow are…

Let $G$ be a connected, simply connected nilpotent Lie group, identified with a real algebraic subgroup of $\mathrm{UT}(n,\mathbb{R})$, and let $\Gamma$ be a lattice in $G$, with $\pi:G\to G/\Gamma$ the quotient map. For a semi-algebraic…

Constructal Law states that a finite-size flow system that persists in time evolves its configuration so as to provide progressively easier access to the currents that flow through it. Classical Constructal theory derives hierarchical flow…

Let $\mathbb K=(K,+,\cdot,v,\Gamma)$ be a valued algebraically closed field of characteristic and $(G,\oplus)$ be a $\mathcal K$-interpretable group that is either locally isomorphic to $(K,+)$ or to $(K,\cdot)$. Then if $\mathcal…

Let $(\mathcal{M},g)$ be a closed Riemannian manifold. The $\textit{ second order approximation}$ to the perturbative renormalization group flow for the nonlinear sigma model (RG-2 flow) is given by : \[ \frac{\partial }{\partial t} \, g(t)…

We identify incompressible planar linear flows that are generalizations of the well known one-parameter family characterized by the ratio of in-plane extension to (out-of-plane) vorticity. The latter `canonical' family is classified into…

Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data…

Let N be an o-minimal structure. In this paper we develop group extension and group cohomology theory over N and use it to describe the N-definable solvable groups. We prove an o-minimal analogue of the Lie-Kolchin-Mal'cev theorem and we…

Let M be a hyperbolizable, nontrivial compression body without toroidal boundary components. In this paper, we characterize which discrete and faithful representations of the fundamental group of M into PSL(2,C) are separable-stable. The…

In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…

We continue our earlier study of finite dimensional definable groups in models of the the model companion of an o-minimal L-theory T expanded by a generic derivation as in [F-K]. We generalize Buium's notion of an algebraic D-group to…

We give an arithmetic criterion which is sufficient to imply the discreteness of various two-generator subgroups of $PSL(2,{\bold C})$. We then examine certain two-generator groups which arise as extremals in various geometric problems in…

Generalizing a result of Furstenberg, we show that for every infinite discrete group $G$, the Bernoulli flow $2^G$ is disjoint from every minimal $G$-flow. From this, we deduce that the algebra generated by the minimal functions…

Let $G$ be a discrete infinite amenable group, which acts from the left on a compact metric space $X$. In this paper, we study the chaotic dynamics exhibited inside and near a minimal center of attraction of $(G,X)$ relative to any…

We consider nilpotent Lie groups for which the derived subgroup is abelian. We equip them with subRiemannian metrics and we study the normal Hamiltonian flow on the cotangent bundle. We show a correspondence between normal trajectories and…