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  • 1
    Electronic Resource
    Electronic Resource
    Determining Asymptotic Behavior from the Dynamics on Attracting Sets (1999)
    Springer
    Journal of dynamics and differential equations 11 (1999), S. 319-331 
    Details
    ISSN: 1572-9222
    Keywords: Global attractors ; inertial manifolds ; exponential attractors ; asymptotic completeness ; connectedness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Two tracking properties for trajectories on attracting sets are studied. We prove that trajectories on the full phase space can be followed arbitrarily closely by skipping from one solution on the global attractor to another. A sufficient condition for asymptotic completeness of invariant exponential attractors is found, obtaining similar results as in the theory of inertial manifolds. Furthermore, such sets are shown to be retracts of the phase space, which implies that they are simply connected.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021933514285
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Global Attractors: Topology and Finite-Dimensional Dynamics (1999)
    Springer
    Journal of dynamics and differential equations 11 (1999), S. 557-581 
    Details
    ISSN: 1572-9222
    Keywords: Global attractors ; inertial manifolds ; exponential attractors ; connectedness
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Many dissipative evolution equations possess a global attractor $$A$$ with finite Hausdorff dimension d. In this paper it is shown that there is an embedding X of $$A$$ into $$\mathbb{R}^N $$ , with N=[2d+2], such that X is the global attractor of some finite-dimensional system on $$\mathbb{R}^N $$ with trivial dynamics on X. This allows the construction of a discrete dynamical system on $$\mathbb{R}^N $$ which reproduces the dynamics of the time T map on $$A$$ and has an attractor within an arbitrarily small neighborhood of X. If the Hausdorff dimension is replaced by the fractal dimension, a similar construction can be shown to hold good even if one restricts to orthogonal projections rather than arbitrary embeddings.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021918004832
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
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