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Dynamics Beyond Uniform Hyperbolicity A Global Geometric And Probabilistic Perspective Christian Bonatti Lorenzo J Daz Marcelo Viana

SKU: BELL-49177452

$ 31.00 ~~$ 45.00~~ (-31%)

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Dynamics Beyond Uniform Hyperbolicity A Global Geometric And Probabilistic Perspective Christian Bonatti Lorenzo J Daz Marcelo Viana instant download after payment.

Publisher: Springer

File Extension: PDF

File size: 31.38 MB

Pages: 384

Author: Christian Bonatti; Lorenzo J. Díaz; Marcelo Viana

ISBN: 9783642060410, 3642060412

Language: English

Year: 2010

Product desciption

Dynamics Beyond Uniform Hyperbolicity A Global Geometric And Probabilistic Perspective Christian Bonatti Lorenzo J Daz Marcelo Viana by Christian Bonatti; Lorenzo J. Díaz; Marcelo Viana 9783642060410, 3642060412 instant download after payment.

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.