Related papers: Integrable nonholonomic geodesic flows on compact …

We show that for any solvable Lie group of real type, any homogeneous Ricci flow solution converges in Cheeger-Gromov topology to a unique non-flat solvsoliton, which is independent of the initial left-invariant metric. As an application,…

We give a formula for the topological pressure of the geodesic flow of a compact rank 1 manifold in terms of the growth of the number of closed hyperbolic (rank 1) geodesics. We derive an equidistribution result for these geodesics with…

In contrast to the Euler-Poincar{\'e} reduction of geodesic flows of left- or right-invariant metrics on Lie groups to the corresponding Lie algebra (or its dual), one can consider the reduction of the geodesic flows to the group itself.…

We define a notion of equivariant non-degeneracy of $G$-maps to introduce the class of equivariantly non-degenerate flows on smooth compact manifolds with compact Lie group action. We prove genericity of this class and use this result to…

We consider nonholonomic systems whose configuration space is the central extension of a Lie group and have left invariant kinetic energy and constraints. We study the structure of the associated Euler-Poincare-Suslov equations and show…

Let N be a nilpotent Lie group and let S be an invariant geometric structure on N (cf. symplectic, complex or hypercomplex). We define a left invariant Riemannian metric on N compatible with S to be "minimal", if it minimizes the norm of…

We describe the local transition probability of a singular diagonal action on the standard non-uniform quotient of $PGL_3$ associated to the type 1 geodesic flow. As a consequence, we deduce the strongly positive recurrence property of the…

The paper is devoted to the group analysis of equations of motion of two-dimensional uniformly stratified rotating fluids used as a basic model in geophysical fluid dynamics. It is shown that the nonlinear equations in question have a…

We introduce a natural subset of the unit tangent bundle of a convex projective manifold, the biproximal unit tangent bundle; it is closed and invariant under the geodesic flow, and we prove that the geodesic flow is topologically mixing on…

In this article we study the Hofer geometry of a compact Lie group $K$ which acts by Hamiltonian diffeomorphisms on a symplectic manifold $M$. Generalized Hofer norms on the Lie algebra of $K$ are introduced and analyzed with tools from…

We prove that every homogeneous flow on a finite-volume homogeneous manifold has countably many independent invariant distributions unless it is conjugate to a linear flow on a torus. We also prove that the same conclusion holds for every…

We study discrete, cocompact, isometric actions of groups on Hadamard spaces, and the induced actions on ideal boundaries. For a class of groups generalizing fundamental groups of three-dimensional graph manifolds, we find a set of…

We discuss canonical transformations relating well-known geodesic flows on the cotangent bundle of the sphere with a set of geodesic flows with quartic invariants. By adding various potentials to the corresponding geodesic Hamiltonians, we…

In this paper, the steady creeping flow equations of a second grade fluid in cartesian coordinates are considered; the equations involve a small parameter related to the dimensionless non--Newtonian coefficient. According to a recently…

We prove an abstract compactness result for gradient flow lines of a non-local unregularized gradient flow equation on a scale Hilbert space. This is the first step towards Floer theory on scale Hilbert spaces.

In this article, we study the dynamics of geodesic flows on Riemannian (not necessarily compact) manifolds with no conjugate points. We prove the Anosov Closing Lemma, the local product structure, and the transitivity of the geodesic flows…

We investigate the Hermitian curvature flow (HCF) of left-invariant metrics on complex unimodular Lie groups. We show that in this setting the flow is governed by the Ricci-flow type equation $\partial_tg_{t}=-{\rm Ric}^{1,1} (g_t)$. The…

We consider a class of dynamical systems on a Lie group $G$ with a left-invariant metric and right-invariant nonholonomic constraints (so called LR systems) and show that, under a generic condition on the constraints, such systems can be…

This is the first part of a series on non-compact groups acting isometrically on compact Lorentz manifolds. This subject was recently investigated by many authors. In the present part we investigate the dynamics of affine, and especially…

In 1966 V.Arnold suggested a group-theoretic approach to ideal hydrodynamics in which the motion of an inviscid incompressible fluid is described as the geodesic flow of the right-invariant $L^2$-metric on the group of volume-preserving…