Smooth Invariant Foliations in Infinite Dimensional Spaces
TLDR
In this article, the authors consider a linear system in Rmfn and show that if each leaf is used as a coordinate, the original system is completely decoupled and the linearization follows easily.About:
This article is published in Journal of Differential Equations.The article was published on 1991-12-01 and is currently open access. It has received 135 citations till now. The article focuses on the topics: Invariant (mathematics) & Homoclinic bifurcation.read more
Citations
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Traveling Waves in Lattice Dynamical Systems
TL;DR: In this article, the existence and stability of traveling waves in lattice dynamical systems, in particular in coupled map lattices and in CMLs, was studied, and it was shown that the traveling wave corresponds to a periodic solution of a nonautonomous periodic differential equation.
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Center Manifolds for Semilinear Equations With Non-dense Domain and Applications to Hopf Bifurcation in Age Structured Models
Pierre Magal,Shigui Ruan +1 more
TL;DR: In this paper, an integrated semigroups Spectral decomposition of the state space Center manifold theory Hopf bifurcation in age structured models has been studied in the literature.
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Smooth Stable and Unstable Manifolds for Stochastic Evolutionary Equations
TL;DR: In this paper, a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of stochastic partial differential equations is presented, and the smoothness of these invariant manifolds is proved.
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Smooth stable and unstable manifolds for stochastic partial differential equations
TL;DR: In this article, a theory of stable and unstable manifolds for infinite dimensional random dynamical systems generated by a class of stochastic partial differential equations is presented, and the smoothness of these invariant manifolds is proved by the Lyapunov-Perron method.
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Persistent homoclinic orbits for a perturbed nonlinear schrodinger equation
TL;DR: In this article, the existence of a symmetric pair of homoclinic orbits for the perturbed NLS equation through an argument that combines Melnikov analysis with a geometric singular perturbation theory for the PDE is established.
References
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Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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Geometric Theory of Semilinear Parabolic Equations
TL;DR: The neighborhood of an invariant manifold near an equilibrium point is a neighborhood of nonlinear parabolic equations in physical, biological and engineering problems as mentioned in this paper, where the neighborhood of a periodic solution is defined by the invariance of the manifold.
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Infinite-Dimensional Dynamical Systems in Mechanics and Physics
TL;DR: In this article, the authors give bounds on the number of degrees of freedom and the dimension of attractors of some physical systems, including inertial manifolds and slow manifolds.
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Asymptotic Behavior of Dissipative Systems
TL;DR: In this article, the authors consider a continuous dynamical system with a global attractor and describe the properties of the flow on the attractor asymptotically smooth and Morse-Smale maps.