Dynamics Beyond Uniform Hyperbolicity

Dynamics Beyond Uniform Hyperbolicity

AngličtinaEbook
Bonatti, Christian
Springer Berlin Heidelberg
EAN: 9783540268444
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Podrobné informace

What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an &quote;infinitesimal&quote; 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.
EAN 9783540268444
ISBN 3540268448
Typ produktu Ebook
Vydavatel Springer Berlin Heidelberg
Datum vydání 30. března 2006
Jazyk English
Země Germany
Autoři Bonatti, Christian; Diaz, Lorenzo J.; Viana, Marcelo
Série Encyclopaedia of Mathematical Sciences
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