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Hardcover ISBN:  9780821841020 
Product Code:  ADVSOV/3 
List Price:  $179.00 
MAA Member Price:  $161.10 
AMS Member Price:  $143.20 
eBook ISBN:  9781470445508 
Product Code:  ADVSOV/3.E 
List Price:  $179.00 
MAA Member Price:  $161.10 
AMS Member Price:  $143.20 
Hardcover ISBN:  9780821841020 
eBook ISBN:  9781470445508 
Product Code:  ADVSOV/3.B 
List Price:  $358.00 $268.50 
MAA Member Price:  $322.20 $241.65 
AMS Member Price:  $286.40 $214.80 

Book DetailsAdvances in Soviet MathematicsVolume: 3; 1991; 254 ppMSC: Primary 15; 34; 60; 70; 81; 82; Secondary 58
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

Articles

M. Blank — Phase space discretization in chaotic dynamical systems

V. Girko — $G$consistent estimates of eigenvalues and eigenvectors of matrices

K. Khanin and E. Vul — Circle homeomorphisms with weak discontinuities

D. Kosygin — Multidimensional KAM theory from the renormalization group viewpoint

G. Levin — Symmetries on a Julia set

M. Missarov — Renormalization group and renormalization theory in padic and adelic scalar models

Ya. Pesin and Ya. Sinai — Spacetime chaos in chains of weakly interacting hyperbolic mappings

Ya. Sinai — Poisson distribution in a geometric problem

S. Zhitomirskaya — Singular spectral properties of a onedimensional Schrödinger operator with almost periodic potential


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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.

Articles

M. Blank — Phase space discretization in chaotic dynamical systems

V. Girko — $G$consistent estimates of eigenvalues and eigenvectors of matrices

K. Khanin and E. Vul — Circle homeomorphisms with weak discontinuities

D. Kosygin — Multidimensional KAM theory from the renormalization group viewpoint

G. Levin — Symmetries on a Julia set

M. Missarov — Renormalization group and renormalization theory in padic and adelic scalar models

Ya. Pesin and Ya. Sinai — Spacetime chaos in chains of weakly interacting hyperbolic mappings

Ya. Sinai — Poisson distribution in a geometric problem

S. Zhitomirskaya — Singular spectral properties of a onedimensional Schrödinger operator with almost periodic potential