Related papers: KAM-rigidity for parabolic affine abelian actions

This paper is concerned with the stickiness of invariant tori obtained by KAM technics (so-called KAM tori) for higher dimensional beam equation. We prove that the KAM tori are sticky, i.e. the solutions starting in the…

Let $p$ be a prime, let $KU_p$ be $p$-complete complex $K$-theory, and let $\mathbb{Z}_p^\times$ denote the group of units in the $p$-adic integers. The $p$-adic Adams operations induce an action of the profinite group $\mathbb{Z}_p^\times$…

We study the perturbative and parametric stability of the QCD predictions for the Callan-Gross ratio $R(x,Q^2)=F_L/F_T$ and azimuthal $\cos(2\varphi)$ asymmetry, $A(x,Q^2)$, in heavy-quark leptoproduction. We review the available…

A Kahler-type form is a symplectic form compatible with an integrable complex structure. Let M be either a torus or a K3-surface equipped with a Kahler-type form. We show that the homology class of any Maslov-zero Lagrangian torus in M has…

A countable discrete group $\Gamma$ is said to be Frobenius stable if a function from the group that is "almost multiplicative" in the point Frobenius norm topology is "close" to a genuine unitary representation in the same topology. The…

We present the most general gauge-invariant action functional for coupled 1- and 2-form gauge fields with kinetic terms in generic dimensions, i.e. dropping eventual contributions that can be added in particular space-time dimensions only…

We study reversibility and strong reversibility of affine automorphisms of the two-torus, written as $f_{A,\bar{a}}(\bar{x})=A\bar{x}+\bar{a} \ (\mathrm{mod}\ \mathbb{Z}^2)$. We derive explicit criteria for the reversibility of such maps in…

In this paper we prove that if two normal affine surfaces $S$ and $S'$ have isomorphic automorphism groups, then every connected algebraic group acting regularly and faithfully on $S$ acts also regularly and faithfully on $S'$. Moreover, if…

We prove that a normal affine surface $V$ over $\bf C$ admits an effective action of a maximal torus ${\bf T}={\bf C}^{*n}$ ($n\le 2$) such that any other effective ${\bf C}^*$-action is conjugate to a subtorus of $\bf T$ in Aut $(V)$, in…

A Riemann surface equipped with its conformal hyperbolic metric is parabolic if and only if the geodesic flow on its unit tangent bundle is ergodic. Let X be a Cantor tree or a blooming Cantor tree Riemann surface. Fix a geodesic pants…

We prove a rigidity property in non-Archimedean dynamics, reminiscent of Zdunik theorem in complex dynamics: every rational map whose equilibrium measure charges an interval in the Berkovich projective line is affine Bernoulli. Our proof is…

In this paper we establish a rigidity property of holomorphic generators by using their local behavior at a boundary point $\tau$ of the open unit disk $\Delta$. Namely, if $f\in\mathrm{Hol}(\Delta,\mathbb{C})$ is the generator of a…

David Aspero asks on the possibility of having Forcing axiom FA_{aleph_2}(K), where K is the class of forcing notions preserving stationarity of subsets of aleph_1 and of aleph_2. We answer negatively, in fact we show the negative result…

We investigate Gaussian actions through the study of their crossed-product von Neumann algebra. The motivational result is Chifan and Ioana's ergodic decomposition theorem for Bernoulli actions (Ergodic subequivalence relations induced by a…

This is a continuation of the series of notes on the dynamics of quadratic polynomials. We show the following Rigidity Theorem: Any combinatorial class contains at most one quadratic polynomial satisfying the secondary limbs condition with…

Let $\Gamma$ be an irreducible lattice of $\Q$-rank $\geq 2$ in a semisimple Lie group of noncompact type. We prove that any action of $\Gamma$ on a $\CAT(0)$ cubical complex has a global fixed point.

We show that it is relatively consistent with ZFC that there exists a hyperfinite type $\mathrm{II}_1$-factor of density character $\aleph_1$ which is not isomorphic to its opposite, does not have any outer automorphisms, and has trivial…

An analog of the Baumslag-Solitar group BS(1,k) naturally acts on the sphere by conformal transformations. The action is not locally rigid in higher dimension, but exhibits a weak form of local rigidity. More precisely, any perturbation…

Let $Aut_{alg}(X)$ be the subgroup of the group of regular automorphisms $Aut(X)$ of an affine algebraic variety $X$ generated by all connected algebraic subgroups. We prove that if $dim X \ge 2$ and if $Aut_{alg}(X)$ is rich enough,…

A hovel is a generalization of the Bruhat-Tits building that is associated to an almost split Kac-Moody group G over a non-Archimedean local field. In particular, G acts strongly transitively on its corresponding hovel $\Delta$ as well as…