Robust unbounded attractors for differential equations in R
نویسندگان
چکیده
We construct unbounded strange attractors for vector fields in R that are robust transitive under uniformly small perturbations. Their geometry is reminiscent of geometric Lorenz and other singular hyperbolic attractors, but they contain no equilibria.
منابع مشابه
Pullback D-attractors for non-autonomous partly dissipative reaction-diffusion equations in unbounded domains
At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.
متن کاملNumerical solution of Fredholm integral-differential equations on unbounded domain
In this study, a new and efficient approach is presented for numerical solution of Fredholm integro-differential equations (FIDEs) of the second kind on unbounded domain with degenerate kernel based on operational matrices with respect to generalized Laguerre polynomials(GLPs). Properties of these polynomials and operational matrices of integration, differentiation are introduced and are ultili...
متن کاملSolving high-order partial differential equations in unbounded domains by means of double exponential second kind Chebyshev approximation
In this paper, a collocation method for solving high-order linear partial differential equations (PDEs) with variable coefficients under more general form of conditions is presented. This method is based on the approximation of the truncated double exponential second kind Chebyshev (ESC) series. The definition of the partial derivative is presented and derived as new operational matrices of der...
متن کاملThe Uniform Attractors for the Nonhomogeneous 2D Navier-Stokes Equations in Some Unbounded Domain
We consider the attractors for the two-dimensional nonautonomous Navier-Stokes equations in some unbounded domain Ω with nonhomogeneous boundary conditions. We apply the so-called uniformly ω-limit compact approach to nonhomogeneous Navier-Stokes equation as well as a method to verify it. Assuming f ∈ Lloc 0, T ;L2 Ω , which is translation compact and φ ∈ C1 b R ;H2 R1 × {±L} asymptotically alm...
متن کاملPeriodic Random Attractors for Stochastic Navier-stokes Equations on Unbounded Domains
This article concerns the asymptotic behavior of solutions to the two-dimensional Navier-Stokes equations with both non-autonomous deterministic and stochastic terms defined on unbounded domains. First we introduce a continuous cocycle for the equations and then prove the existence and uniqueness of tempered random attractors. We also characterize the structures of the random attractors by comp...
متن کامل