Advances in Soviet Mathematics 1991; 254 pp; hardcover Volume: 3 ISBN10: 0821841025 ISBN13: 9780821841020 List Price: US$170 Member Price: US$136 Order Code: ADVSOV/3
 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 infinitedimensional 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 onedimensional 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. Table of Contents  M. L. Blank  Phase space discretization in chaotic dynamical systems
 V. L. Girko  \(G\)consistent estimates of eigenvalues and eigenvectors of matrices
 K. M. Khanin and E. B. Vul  Circle homeomorphisms with weak discontinuities
 D. V. Kosygin  Multidimensional KAM theory from the renormalization group viewpoint
 G. M. Levin  Symmetries on a Julia set
 M. D. Missarov  Renormalization group and renormalization theory in padic and adelic scalar models
 Ya. B. Pesin and Ya. G. Sinaĭ  Spacetime chaos in chains of weakly interacting hyperbolic mappings
 Ya. G. Sinaĭ  Poisson distribution in a geometric problem
 S. Ya. Zhitomirskaya  Singular spectral properties of a onedimensional Schrödinger operator with almost periodic potential
