CRM Proceedings & Lecture Notes 2004; 347 pp; softcover Volume: 37 ISBN10: 0821833294 ISBN13: 9780821833292 List Price: US$120 Member Price: US$96 Order Code: CRMP/37
 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. Readership Graduate students and research mathematicians interested in integrable systems. Table of Contents  Á. Ballesteros, F. J. Herranz, F. Musso, and O. Ragnisco  Superintegrable deformations of the SmorodinskyWinternitz Hamiltonian
 F. Calogero and J.P. Françoise  Isochronous motions galore: Nonlinearly coupled oscillators with lots of isochronous solutions
 T. L. Curtright and C. K. Zachos  Nambu dynamics, deformation quantization, and superintegrability
 C. Gonera  Maximally superintegrable systems of Winternitz type
 S. Gravel  Cubic integrals of motion and quantum superintegrability
 J. Harnad and O. Yermolayeva  Superintegrability, Lax matrices and separation of variables
 F. J. Herranz, Á. Ballesteros, M. Santander, and T. SanzGil  Maximally superintegrable SmorodinskyWinternitz systems on the \(N\)dimensional sphere and hyperbolic spaces
 A. Kokotov and D. Korotkin  Invariant Wirtinger projective connection and Taufunctions on spaces of branched coverings
 L. G. Mardoyan  Dyonoscillator duality. Hidden symmetry of the YangCoulomb monopole
 P. Desrosiers, L. Lapointe, and P. Mathieu  Supersymmetric CalogeroMoserSutherland models: Superintegrability structure and eigenfunctions
 W. Miller, Jr.  Complete sets of invariants for classical systems
 A. G. Nikitin  Higherorder symmetry operators for Schrödinger equation
 A. V. Penskoi  Symmetries and Lagrangian timediscretizations of Euler equations
 L. G. Mardoyan, G. S. Pogosyan, and A. N. Sissakian  Two exactlysolvable problems in onedimensional quantum mechanics on circle
 M. F. Rañada and M. Santander  Higherorder superintegrability of a rational oscillator with inversely quadratic nonlinearities: Euclidean and nonEuclidean cases
 F. Finkel, D. GómezUllate, A. GonzálezLópez, M. A. Rodríguez, and R. Zhdanov  A survey of quasiexactly solvable systems and spin CalogeroSutherland models
 M. Sheftel  On the classification of thirdorder integrals of motion in twodimensional quantum mechanics
 R. G. McLenaghan, R. G. Smirnov, and D. The  Towards a classification of cubic integrals of motion
 K. Takasaki  Integrable systems whose spectral curves are the graph of a function
 P. Tempesta  On superintegrable systems in \(E_2\): Algebraic properties and symmetry preserving discretization
 A. V. Turbiner  Perturbations of integrable systems and DysonMehta integrals
 Y. Uwano  Separability and the BirkhoffGustavson normalization of the perturbed harmonic oscillators with homogeneous polynomial potentials
 J. Bérubé and P. Winternitz  Integrability and superintegrability without separability
 T. Wolf  Applications of CRACK in the classification of integrable systems
 G. A. Grünbaum and M. Yakimov  The prolate spheroidal phenomenon as a consequence of bispectrality
 O. Yermolayeva  On a trigonometric analogue of AtiyahHitchin bracket
 A. Zhalij and R. Zhdanov  Separation of variables in timedependent Schrödinger equations
 M. Znojil  New types of solvability in PT symmetric quantum theory
