Softcover ISBN:  9780821833292 
Product Code:  CRMP/37 
List Price:  $126.00 
MAA Member Price:  $113.40 
AMS Member Price:  $100.80 
eBook ISBN:  9781470439514 
Product Code:  CRMP/37.E 
List Price:  $126.00 
MAA Member Price:  $113.40 
AMS Member Price:  $100.80 
Softcover ISBN:  9780821833292 
eBook: ISBN:  9781470439514 
Product Code:  CRMP/37.B 
List Price:  $252.00 $189.00 
MAA Member Price:  $226.80 $170.10 
AMS Member Price:  $201.60 $151.20 
Softcover ISBN:  9780821833292 
Product Code:  CRMP/37 
List Price:  $126.00 
MAA Member Price:  $113.40 
AMS Member Price:  $100.80 
eBook ISBN:  9781470439514 
Product Code:  CRMP/37.E 
List Price:  $126.00 
MAA Member Price:  $113.40 
AMS Member Price:  $100.80 
Softcover ISBN:  9780821833292 
eBook ISBN:  9781470439514 
Product Code:  CRMP/37.B 
List Price:  $252.00 $189.00 
MAA Member Price:  $226.80 $170.10 
AMS Member Price:  $201.60 $151.20 

Book DetailsCRM Proceedings & Lecture NotesVolume: 37; 2004; 347 ppMSC: Primary 81; 37; 22
Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This proceedings volume grew out of the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathématiques in Montréal (Quebec). The meeting brought together scientists working in the area of finitedimensional integrable systems to discuss new developments in this active field of interest.
Properties possessed by these systems are manifold. In classical mechanics, they have stable periodic orbits (all finite orbits are periodic). In quantum mechanics, all known superintegrable systems have been shown to be exactly solvable. Their energy spectrum is degenerate and can be calculated algebraically. The spectra of superintegrable systems may also have other interesting properties, for example, the saturation of eigenfunction norm bounds.
Articles in this volume cover several (overlapping) areas of research, including:
– Standard superintegrable systems in classical and quantum mechanics.
– Superintegrable systems with higherorder or nonpolynomial integrals.
– New types of superintegrable systems in classical mechanics.
– Superintegrability, exact and quasiexact solvability in standard and PTsymmetric quantum mechanics.
– Quantum deformation, Nambu dynamics and algebraic perturbation theory of superintegrable systems.
– Computer assisted classification of integrable equations.
The volume is suitable for graduate students and research mathematicians interested in integrable systems.
Titles in this series are copublished with the Centre de Recherches Mathématiques.
ReadershipGraduate students and research mathematicians interested in integrable systems.

Table of Contents

Chapters

Superintegrable deformations of the Smorodinsky–Winternitz Hamiltonian

Isochronous motions galore: Nonlinearly coupled oscillators with lots of isochronous solutions

Nambu dynamics, deformation quantization, and superintegrability

Maximally superintegrable systems of Winternitz type

Cubic integrals of motion and quantum superintegrability

Superintegrability, Lax matrices and separation of variables

Maximally superintegrable Smorodinsky–Winternitz systems on the $N$dimensional sphere and hyperbolic spaces

Invariant Wirtinger projective connection and Taufunctions on spaces of branched coverings

Dyonoscillator duality. Hidden symmetry of the YangCoulomb monopole

Supersymmetric CalogeroMoserSutherland models: Superintegrability structure and eigenfunctions

Complete sets of invariants for classical systems

Higherorder symmetry operators for Schrödinger equation

Symmetries and Lagrangian timediscretizations of Euler equations

Two exactlysolvable problems in onedimensional quantum mechanics on circle

Higherorder superintegrability of a rational oscillator with inversely quadratic nonlinearities: Euclidean and nonEuclidean cases

A survey of quasiexactly solvable systems and spin Calogero–Sutherland models

On the classification of thirdorder integrals of motion in twodimensional quantum mechanics

Towards a classification of cubic integrals of motion

Integrable systems whose spectral curves are the graph of a function

On superintegrable systems in $E_2$: Algebraic properties and symmetry preserving discretization

Perturbations of integrable systems and DysonMehta integrals

Separability and the Birkhoff–Gustavson normalization of the perturbed harmonic oscillators with homogeneous polynomial potentials

Integrability and superintegrability without separability

Applications of CRACK in the classification of integrable systems

The prolate spheroidal phenomenon as a consequence of bispectrality

On a trigonometric analogue of Atiyah–Hitchin bracket

Separation of variables in timedependent Schrödinger equations

New types of solvability in PT symmetric quantum theory


RequestsReview Copy – for publishers of book reviewsAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Requests
Superintegrable systems are integrable systems (classical and quantum) that have more integrals of motion than degrees of freedom. Such systems have many interesting properties. This proceedings volume grew out of the Workshop on Superintegrability in Classical and Quantum Systems organized by the Centre de Recherches Mathématiques in Montréal (Quebec). The meeting brought together scientists working in the area of finitedimensional integrable systems to discuss new developments in this active field of interest.
Properties possessed by these systems are manifold. In classical mechanics, they have stable periodic orbits (all finite orbits are periodic). In quantum mechanics, all known superintegrable systems have been shown to be exactly solvable. Their energy spectrum is degenerate and can be calculated algebraically. The spectra of superintegrable systems may also have other interesting properties, for example, the saturation of eigenfunction norm bounds.
Articles in this volume cover several (overlapping) areas of research, including:
– Standard superintegrable systems in classical and quantum mechanics.
– Superintegrable systems with higherorder or nonpolynomial integrals.
– New types of superintegrable systems in classical mechanics.
– Superintegrability, exact and quasiexact solvability in standard and PTsymmetric quantum mechanics.
– Quantum deformation, Nambu dynamics and algebraic perturbation theory of superintegrable systems.
– Computer assisted classification of integrable equations.
The volume is suitable for graduate students and research mathematicians interested in integrable systems.
Titles in this series are copublished with the Centre de Recherches Mathématiques.
Graduate students and research mathematicians interested in integrable systems.

Chapters

Superintegrable deformations of the Smorodinsky–Winternitz Hamiltonian

Isochronous motions galore: Nonlinearly coupled oscillators with lots of isochronous solutions

Nambu dynamics, deformation quantization, and superintegrability

Maximally superintegrable systems of Winternitz type

Cubic integrals of motion and quantum superintegrability

Superintegrability, Lax matrices and separation of variables

Maximally superintegrable Smorodinsky–Winternitz systems on the $N$dimensional sphere and hyperbolic spaces

Invariant Wirtinger projective connection and Taufunctions on spaces of branched coverings

Dyonoscillator duality. Hidden symmetry of the YangCoulomb monopole

Supersymmetric CalogeroMoserSutherland models: Superintegrability structure and eigenfunctions

Complete sets of invariants for classical systems

Higherorder symmetry operators for Schrödinger equation

Symmetries and Lagrangian timediscretizations of Euler equations

Two exactlysolvable problems in onedimensional quantum mechanics on circle

Higherorder superintegrability of a rational oscillator with inversely quadratic nonlinearities: Euclidean and nonEuclidean cases

A survey of quasiexactly solvable systems and spin Calogero–Sutherland models

On the classification of thirdorder integrals of motion in twodimensional quantum mechanics

Towards a classification of cubic integrals of motion

Integrable systems whose spectral curves are the graph of a function

On superintegrable systems in $E_2$: Algebraic properties and symmetry preserving discretization

Perturbations of integrable systems and DysonMehta integrals

Separability and the Birkhoff–Gustavson normalization of the perturbed harmonic oscillators with homogeneous polynomial potentials

Integrability and superintegrability without separability

Applications of CRACK in the classification of integrable systems

The prolate spheroidal phenomenon as a consequence of bispectrality

On a trigonometric analogue of Atiyah–Hitchin bracket

Separation of variables in timedependent Schrödinger equations

New types of solvability in PT symmetric quantum theory