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Non-autonomous 2D Navier–Stokes system with a simple global attractor and some averaging problems

V. V. Chepyzhov, M. I. Vishik (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We study the global attractor of the non-autonomous 2D Navier–Stokes system with time-dependent external force g(x,t). We assume that g(x,t) is a translation compact function and the corresponding Grashof number is small. Then the global attractor has a simple structure: it is the closure of all the values of the unique bounded complete trajectory of the Navier–Stokes system. In particular, if g(x,t) is a quasiperiodic function with respect to t, then the attractor is a continuous image...

Nonconventional limit theorems in averaging

Yuri Kifer (2014)

Annales de l'I.H.P. Probabilités et statistiques

We consider “nonconventional” averaging setup in the form d X ε ( t ) d t = ε B ( X ε ( t ) , 𝛯 ( q 1 ( t ) ) , 𝛯 ( q 2 ( t ) ) , ... , 𝛯 ( q ℓ ( t ) ) ) where 𝛯 ( t ) , t ≥ 0 is either a stochastic process or a dynamical system with sufficiently fast mixing while q j ( t ) = α j t , α 1 l t ; α 2 l t ; ⋯ l t ; α k and q j , j = k + 1 , ... , ℓ grow faster than linearly. We show that the properly normalized error term in the “nonconventional” averaging principle is asymptotically Gaussian.

Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy

Javier Ribón (2009)

Annales de l’institut Fourier

The formal class of a germ of diffeomorphism ϕ is embeddable in a flow if ϕ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at ℂ n ( n > 1 ) whose formal class is non-embeddable. The examples are inside a family in which the non-embeddability is of geometrical type. The proof relies on the properties of some linear functional operators that we obtain through the study of polynomial families of diffeomorphisms...

Nonfibered knots and representation shifts

Daniel S. Silver, Susan G. Williams (2009)

Banach Center Publications

A conjecture of [swTAMS] states that a knot is nonfibered if and only if its infinite cyclic cover has uncountably many finite covers. We prove the conjecture for a class of knots that includes all knots of genus 1, using techniques from symbolic dynamics.

Non-holonomic mechanical systems in jet bundles.

Manuel de León, David Martín de Diego (1996)

Extracta Mathematicae

In this paper we present a geometrical formulation for Lagrangian systems subjected to non-holonomic constraints in terms of jet bundles. Cosymplectic geometry and almost product structures are used to obtained the constrained dynamics without using Lagrange multipliers method.

Nonhyperbolic one-dimensional invariant sets with a countably infinite collection of inhomogeneities

Chris Good, Robin Knight, Brian Raines (2006)

Fundamenta Mathematicae

We examine the structure of countable closed invariant sets under a dynamical system on a compact metric space. We are motivated by a desire to understand the possible structures of inhomogeneities in one-dimensional nonhyperbolic sets (inverse limits of finite graphs), particularly when those inhomogeneities form a countable set. Using tools from descriptive set theory we prove a surprising restriction on the topological structure of these invariant sets if the map satisfies a weak repelling or...

Currently displaying 2541 – 2560 of 4762