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  • 1995-1999  (3)
  • 1930-1934
  • 1999  (3)
  • exponential attractors  (2)
  • Callosotomy  (1)
  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Journal of dynamics and differential equations 11 (1999), S. 319-331 
    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
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Journal of dynamics and differential equations 11 (1999), S. 557-581 
    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
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  • 3
    ISSN: 1432-1106
    Keywords: Key words Bimanual coordination ; Callosotomy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Medicine
    Notes: Abstract  We examined bimanual coordination in a patient before and after each stage of callosotomy surgery. We tested how well the patient coordinated movement direction between the hands. The patient drew symmetrical or asymmetrical figures simultaneously with both hands. Before surgery, symmetrical figures were drawn well and asymmetrical figures were drawn poorly. Following anterior callosotomy, the drawings improved slightly. Symmetrical figures were still drawn well, and asymmetrical ones were still drawn poorly. Thus, spatial integration remained intact despite the loss of interhemispheric communication between frontal cortical sites. After posterior callosotomy, spatial coordination deteriorated significantly. Mirror-image drawings became less symmetrical, while asymmetrical drawings improved. These data indicate that the posterior callosum mediates the coordination of direction information between the hands during bimanual movements. Given the topographical organization of the corpus callosum, this integration is likely carried out by parietal cortex.
    Type of Medium: Electronic Resource
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