**Advances in Soviet Mathematics**

1991;
254 pp;
Hardcover

MSC: Primary 15; 34; 60; 70; 81; 82;
Secondary 58; 62

**Print ISBN: 978-0-8218-4102-0
Product Code: ADVSOV/3**

List Price: $170.00

Individual Member Price: $136.00

# Dynamical Systems and Statistical Mechanics

Share this page *Edited by *
*Ya. G. Sinaĭ*

Dynamical systems and statistical mechanics have been developing in close
interaction during the past decade, and the papers in this book attest to the
productiveness of this interaction.

The first paper in the collection contains a new result in the theory of
quantum chaos, a burgeoning line of inquiry that combines mathematics and
physics and is likely in time to produce many new connections and
applications. Another paper, related to the renormalization group method for
the study of maps of the circle with singularities due to a jump in the
derivative, demonstrates that the fixed point of the renormgroup can
be sufficiently described in this case. In certain situations, the renormgroup
methods work better than the traditional KAM method.

Other topics covered include thermodynamic formalism for certain
infinite-dimensional dynamical systems, numerical simulation of dynamical
systems with hyperbolic behavior, periodic points of holomorphic maps, the
theory of random media, statistical properties of the leading eigenvalue in
matrix ensembles of large dimension, spectral properties of the one-dimensional
Schrödinger operator. This volume will appeal to many readers, as it
covers a broad range of topics and presents a view of the some of the frontier
research in the Soviet Union today.