Téléchargez le livre : Dynamics Beyond Uniform Hyperbolicity

Dynamics Beyond Uniform Hyperbolicity

A Global Geometric and Probabilistic Perspective de

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Éditeur :

Springer


Paru le : 2006-03-30

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Description
What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an "infinitesimal" evolution rule is known. Examples and applications arise from all branches of science and technology, like physics, chemistry, economics, ecology, communications, biology, computer science, or meteorology, to mention just a few. These systems have in common the fact that each possible state may be described by a finite (or infinite) number of observable quantities, like position, velocity, temperature, concentration, population density, and the like. Thus, m the space of states (phase space) is a subset M of an Euclidean space M . Usually, there are some constraints between these quantities: for instance, for ideal gases pressure times volume must be proportional to temperature. Then the space M is often a manifold, an n-dimensional surface for some n < m. For continuous time systems, the evolution rule may be a differential eq- tion: to each state x G M one associates the speed and direction in which the system is going to evolve from that state. This corresponds to a vector field X(x) in the phase space. Assuming the vector field is sufficiently regular, for instance continuously differentiable, there exists a unique curve tangent to X at every point and passing through x: we call it the orbit of x.
Pages
384 pages
Collection
n.c
Parution
2006-03-30
Marque
Springer
EAN papier
9783540220664
EAN PDF
9783540268444
Informations sur l'ebook
Nombre pages copiables
3
Nombre pages imprimables
38
Taille du fichier
20275 Ko
Prix
168,79 €

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