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STABLE ERGODICITY FOR PARTIALLY HYPERBOLIC ATTRACTORS WITH NEGATIVE CENTRAL EXPONENTS
PARTIALLY HYPERBOLIC STABLE ERGODICITY
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2015/9/29
We establish stable ergodicity of diffeomorphisms with
partially hyperbolic attractors whose Lyapunov exponents along
the central direction are all negative with respect to invariant SRBmeasur...
Chaotic attractors of relaxation oscillators
relaxation oscillators Chaotic attractors
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2015/8/25
We develop a general technique for proving the existence of chaotic attractors
for three-dimensional vector fields with two time scales. Our results connect
two important areas of dynamical systems:...
Random Attractors for Stochastic Wave Equations with Critical Exponents on Rn
Stochastic Wave Equations Random Attractors
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2015/4/3
Outline
• Stochastic wave equations on Rn.
• Random attractors theory.
• Random absorbing sets for wave equations.
• Pullback asymptotic compactness.
• Existence of ...
Decay of correlations for maps with uniformly contracting fibers and logarithm law for singular hyperbolic attractors
partial hyperbolicity singular-hyperbolicity recurrence decay of correlations local dimension hitting times
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2012/4/23
We consider two dimensional maps preserving a foliation which is uniformly contracting and a one dimensional associated quotient map having exponential convergence to equilibrium (iterates of Lebesgue...
Continuity of attractors for a nonlinear parabolic problem with terms concentrating in the boundary
Partial differential equations on infinite-dimensional spaces asymptotic behavior of solutions attractors singular perturbations concentrating terms
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2012/4/17
We analyze the dynamics of the flow generated by a nonlinear parabolic problem when some reaction and potential terms are concentrated in a neighborhood of the boundary. We assume that this neighborho...
The Existence of Periodic Solution and Periodic Attractors
Non-autonomous Nonclassical Periodic Galerkin approximate
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2011/10/19
This paper is concerned with the dynamical behavior of a class of nonclassical diffusion equations Firstly, the existence of periodic solutions is established by using the Galerkin approximate method ...
Global and trajectory attractors for a nonlocal Cahn-Hilliard-Navier-Stokes system
Navier-Stokes equations nonlocal Cahn-Hilliard equations incompressible binary fluids global attractors
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2011/9/23
Abstract: The Cahn-Hilliard-Navier-Stokes system is based on a well-known diffuse interface model and describes the evolution of an incompressible isothermal mixture of binary fluids. A nonlocal varia...
Dimension of attractors and invariant sets of damped wave equations in unbounded domains
damped wave equation invariant set attractor dimension
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2011/9/5
Abstract: Under fairly general assumptions, we prove that every compact invariant set $\mathcal I$ of the semiflow generated by the semilinear damped wave equation u_{tt}+\alpha u_t+\beta(x)u-\Deltau ...
Pullback attractors for a singularly nonautonomous plate equation
pullback attractors nonautonomous plate equation upper-semicontinuity
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2011/2/24
We consider the family of singularly nonautonomous plate equation with structural damping
utt + a(t, x)ut + (−)ut + (−)2u + u = f(u),in a bounded domain ⊂ Rn, with Navier bounda...
Global attractors for the one dimensional wave equation with displacement dependent damping
Attractors wave equations
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2011/2/24
We study the long-time behavior of solutions of the one dimensional wave equation with nonlinear damping coefficient. We prove that if the damping coefficient function is strictly
positive near the o...
A characterization of compact operators via the non-connectedness of the attractors of a family of IFSs
compact operators the non-connectedness family of IFSs
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2010/11/8
In this paper we present a result which establishes a connection between the theory of compact operators and the theory of iterated function systems. For a Banach space X, S and T bounded linear oper...
Finite dimensional global and exponential attractors for a coupled time-dependent Ginzburg-Landau equations for atomic Fermi gases near the BCS-BEC crossover
Finite dimensional global exponential attractors
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2010/11/9
We study a coupled nonlinear evolution system arising from the Ginzburg-Landau theory for atomic Fermi gases near the BCS-BEC crossover. First, we prove that the initial boundary value problem genera...
Random Attractors for Sto chastic Reaction-Diffusion Equations on Unb ounded Domains
Sto chastic Reaction-Diffusion Equations Domains
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2015/4/3
When Ω is unb ounded the time-t map is no longer
compact, but even i n this case, if g decays sufficiently fast
at infinity, asymptotic compactness of orbits and hence
the existence of a comp...
On riddled sets and bifurcations of chaotic attractors
Riddling basins coupled maps blow out bifurcations
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2010/9/15
Coupled systems provide us examples of blowout bifurcations and these maps have parameter values at which there are attractors which are a filled-in quadrilateral and, simultaneously, the synchronized...
EXPONENTIAL ATTRACTORS OF THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN
Exponential attractor Ginzbur
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2007/12/11
In this paper, the existence of the exponential attractors for the Ginzburg-Landau-BBM equations in an unbounded domain is proved by using weighted function and squeezing property.