相关论文: Discrete orbits and special subgroups of $\Diff$

We define a natural topology on the collection of (equivalence classes up to scaling of) locally finite measures on a homogeneous space and prove that in this topology, pushforwards of certain infinite volume orbits equidistribute in the…

This is a survey on the local structure about a fixed point of discrete finite-dimensional holomorphic dynamical systems, discussing in particular the existence of local topological conjugacies to normal forms, and the structure of local…

Recently, Steinberg used discrete Morse theory to give a new proof of a theorem of Symonds that the orbit space of the poset of nontrivial $p$-subgroups of a finite group is contractible. We extend Steinberg's argument in two ways, covering…

In this paper we study the general concept of integrability in the broad sense within the frame of differential Galois theory. We concentrate on the gradient systems which are not integrable. In spite of it, if we consider them as the real…

Group based moving frames have a wide range of applications, from the classical equivalence problems in differential geometry to more modern applications such as computer vision. Here we describe what we call a discrete group based moving…

In this paper we prove a new characterization of the distinguished unipotent orbits of a connected reductive group over an algebraically closed field of characteristic 0. For classical groups we prove the characterization by a combinatorial…

A notion of implicit difference equation on a Lie groupoid is introduced and an algorithm for extracting the integrable part (backward or/and forward) is formulated. As an application, we prove that discrete Lagrangian dynamics on a Lie…

A locally normal subgroup in a topological group is a subgroup whose normaliser is open. In this paper, we provide a detailed description of the large-scale structure of closed locally normal subgroups of complete Kac-Moody groups over…

We study the topology of orbits of dynamical systems defined by finite-dimensional representations of nilpotent Lie groups. Thus, the following dichotomy is established: either the interior of the set of regular points is dense in the…

The article investigates systems of differential-difference equations of hyperbolic type, integrable in sense of Darboux. The concept of a complete set of independent characteristic integrals underlying Darboux integrability is discussed. A…

We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…

We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics of rank two cluster algebras. These systems exhibit behavior associated with integrability, namely preservation of a symplectic form,…

We study the properties of orthogonality to the constants and disintegration for autonomous algebraic differential equations. We present a criterion of orthogonality to the constants for absolutely irreducible real $D$-varieties relying on…

We introduce invertible subalgebras of local operator algebras on lattices. An invertible subalgebra is defined to be one such that every local operator can be locally expressed by elements of the inveritible subalgebra and those of the…

We study spatial discretizations of dynamical systems: is it possible to recover some dynamical features of a system from numerical simulations? Here, we tackle this issue for the simplest algorithm possible: we compute long segments of…

This paper is about nilpotent orbits of reductive groups over local non-Archimedean fields. In this paper we will try to identify for which groups there are only finitely many nilpotent orbits, for which groups the nilpotent orbits are…

A number of techniques have been developed to perturb the dynamics of $C^1$-diffeomorphisms and to modify the properties of their periodic orbits. For instance, one can locally linearize the dynamics, change the tangent dynamics, or create…

We solve the regularity problem for Milnor's infinite dimensional Lie groups in the $C^0$-topological context, and provide necessary and sufficient regularity conditions for the (standard) $C^k$-topological setting. We prove that the…

In this note we study countable subgroups of the full group of a measure preserving equivalence relation. We provide various constraints on the group structure, the nature of the action, and on the measure of fixed point sets, that imply…

We establish plurisubharmonicity of envelopes of certain classical disc functionals on locally irreducible complex spaces, thereby generalizing the corresponding results for complex manifolds. We also find new formulae expressing the…