# The asymptotic completeness of inertial manifolds

@article{Robinson1996TheAC, title={The asymptotic completeness of inertial manifolds}, author={James C. Robinson}, journal={Nonlinearity}, year={1996}, volume={9}, pages={1325-1340} }

An investigation of the asymptotic completeness property for inertial manifolds leads to the concept of `flow-normal hyperbolicity', which is more natural in this case than the traditional form of normal hyperbolicity derived from the linearized flow near the manifold. An example shows that without flow-normal hyperbolicity asymptotic completeness cannot be guaranteed. The analysis also yields a new result on the asymptotic equivalence of ordinary differential equations.

## 49 Citations

### Some closure results for inertial manifolds

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Suppose that the family of evolution equationsdu/dt+Au+fN(u)=0 possesses inertial manifolds of the same dimension for a sequence of nonlinear termsfN withfN →f in the C0 norm. Conditions are found to…

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### Tracking properties of trajectories on random attracting Sets

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The theory of random attracting sets highlights interesting properties of the asymptotic behaviour of some stochastic differential equations. In this paper some results on the relation between the…

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We study asymptotically compact nonautonomous dynamical systems given by abstract cocycles in Banach spaces. Our main assumptions are given by a squeezing property in a quadratic cone ﬁeld (given by…

### Geometric theory of inertial manifolds for compact cocycles in Banach spaces

- Mathematics
- 2020

We present a geometric theory of inertial manifolds for compact cocycles (non-autonomous dynamical systems), which satisfy a certain squeezing property with respect to a family of quadratic Lyapunov…

### Pullback Attracting Inertial Manifolds for Nonautonomous Dynamical Systems

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In this paper we present an abstract approach to inertial manifolds for nonautonomous dynamical systems. Our result on the existence of inertial manifolds requires only two geometrical assumptions,…

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In this paper, stochastic inertial manifold for damped wave equations subjected to additive white noise is constructed by the Lyapunov–Perron method. It is proved that when the intensity of noise…

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