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02751nam a22004695i 4500 |
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978-3-642-14258-1 |
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DE-He213 |
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20151204165312.0 |
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cr nn 008mamaa |
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100825s2010 gw | s |||| 0|eng d |
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|a 9783642142581
|9 978-3-642-14258-1
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|a 10.1007/978-3-642-14258-1
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|a 515.39
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|a 515.48
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|a Pötzsche, Christian.
|e author.
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|a Geometric Theory of Discrete Nonautonomous Dynamical Systems
|h [electronic resource] /
|c by Christian Pötzsche.
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|a Berlin, Heidelberg :
|b Springer Berlin Heidelberg,
|c 2010.
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|a XXIV, 399 p. 17 illus., 2 illus. in color.
|b online resource.
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|a text
|b txt
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|a computer
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|a online resource
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|a text file
|b PDF
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 2002
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|a Nonautonomous Dynamical Systems -- Nonautonomous Difference Equations -- Linear Difference Equations -- Invariant Fiber Bundles -- Linearization.
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|a Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.
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|a Mathematics.
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|a Dynamics.
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|a Ergodic theory.
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|a Mathematics.
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|a Dynamical Systems and Ergodic Theory.
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| 710 |
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|a SpringerLink (Online service)
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|t Springer eBooks
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|i Printed edition:
|z 9783642142574
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| 830 |
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|a Lecture Notes in Mathematics,
|x 0075-8434 ;
|v 2002
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|u http://dx.doi.org/10.1007/978-3-642-14258-1
|z Full Text via HEAL-Link
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|a ZDB-2-SMA
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|a ZDB-2-LNM
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|a Mathematics and Statistics (Springer-11649)
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