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Nonuniform Hyperbolicity - Dynamics of Systems with Nonzero Lyapunov Exponents (Hardcover)
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Nonuniform Hyperbolicity - Dynamics of Systems with Nonzero Lyapunov Exponents (Hardcover)
Series: Encyclopedia of Mathematics and its Applications
Expected to ship within 10 - 15 working days
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Designed to work as a reference and as a supplement to an advanced
course on dynamical systems, this book presents a self-contained
and comprehensive account of modern smooth ergodic theory. Among
other things, this provides a rigorous mathematical foundation for
the phenomenon known as deterministic chaos - the appearance of
'chaotic' motions in pure deterministic dynamical systems. A
sufficiently complete description of topological and ergodic
properties of systems exhibiting deterministic chaos can be deduced
from relatively weak requirements on their local behavior known as
nonuniform hyperbolicity conditions. Nonuniform hyperbolicity
theory is an important part of the general theory of dynamical
systems. Its core is the study of dynamical systems with nonzero
Lyapunov exponents both conservative and dissipative, in addition
to cocycles and group actions. The results of this theory are
widely used in geometry (e.g., geodesic flows and Teichmuller
flows), in rigidity theory, in the study of some partial
differential equations (e.g., the Schroedinger equation), in the
theory of billiards, as well as in applications to physics,
biology, engineering, and other fields.
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