close
1.

図書

図書
Kai-Seng Chou, Xi-Ping Zhu
出版情報: Boca Raton, Flo. : Chapman & Hall/CRC, c2001  ix, 255 p. ; 24 cm
所蔵情報: loading…
目次情報: 続きを見る
Preface
Basic Results / 1:
Short time existence / 1.1:
Facts from the parabolic theory / 1.2:
The evolution of geometric quantities / 1.3:
Invariant Solutions for the Curve Shortening Flow / 2:
Travelling waves / 2.1:
Spirals / 2.2:
The support function of a convex curve / 2.3:
Self-similar solutions / 2.4:
The Curvature-Eikonal Flow for Convex Curves / 3:
Blaschke Selection Theorem / 3.1:
Preserving convexity and shrinking to a point / 3.2:
Gage-Hamilton Theorem / 3.3:
The contracting case of the ACEF / 3.4:
The stationary case of the ACEF / 3.5:
The expanding case of the ACEF / 3.6:
The Convex Generalized Curve Shortening Flow / 4:
Results from the Brunn-Minkowski Theory / 4.1:
The AGCSF for [sigma] in (1/3, 1) / 4.2:
The affine curve shortening flow / 4.3:
Uniqueness of self-similar solutions / 4.4:
The Non-convex Curve Shortening Flow / 5:
An isoperimetric ratio / 5.1:
Limits of the rescaled flow / 5.2:
Classification of singularities / 5.3:
A Class of Non-convex Anisotropic Flows / 6:
The decrease in total absolute curvature / 6.1:
The existence of a limit curve / 6.2:
Shrinking to a point / 6.3:
A whisker lemma / 6.4:
The convexity theorem / 6.5:
Embedded Closed Geodesics on Surfaces / 7:
Basic results / 7.1:
The limit curve / 7.2:
Convergence to a geodesic / 7.3:
The Non-convex Generalized Curve Shortening Flow / 8:
The number of convex arcs / 8.1:
Removal of interior singularities / 8.3:
The almost convexity theorem / 8.5:
Bibliography
Index
Preface
Basic Results / 1:
Short time existence / 1.1:
2.

図書

図書
Boris A. Kupershmidt
出版情報: Providence, R.I. : American Mathematical Society, c2000  xviii, 600 p. ; 27 cm
シリーズ名: Mathematical surveys and monographs ; v. 78
所蔵情報: loading…
3.

図書

図書
Gordon E. Swaters
出版情報: Boca Raton, Fla. ; London : Chapman & Hall/CRC, c2000  274 p. ; 25 cm
シリーズ名: Chapman & Hall/CRC monographs and surveys in pure and applied mathematics ; 102
所蔵情報: loading…
4.

図書

図書
Michael Struwe
出版情報: Berlin : Springer, c2000  xviii, 274 p. ; 25 cm
シリーズ名: Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 34
所蔵情報: loading…
5.

図書

図書
Ernst Hairer, Christian Lubich, Gerhard Wanner
出版情報: Berlin ; Tokyo : Springer, c2002  xiii, 515 p. ; 24 cm
シリーズ名: Springer series in computational mathematics ; v. 31
所蔵情報: loading…
6.

図書

図書
Olivier Babelon, Denis Bernard, Michel Talon
出版情報: Cambridge : Cambridge University Press, 2003  xi, 602 p. ; 26 cm
シリーズ名: Cambridge monographs on mathematical physics
所蔵情報: loading…
目次情報: 続きを見る
Introduction / 1:
Integrable dynamical systems / 2:
Synopsis of integrable systems / 2.1:
Algebraic methods / 4:
The Liouville theorem / 5:
Analytical methods
The closed Toda chain / 2.3:
Action-angle variables
The Calogero-Moser model / 7:
Lax pairs / 8:
Isomonodromic deformations
Grassmannian and integrable hierarchies / 2.5:
Existence of an r-matrix
The KP hierarchy / 10:
Commuting flows / 11:
The KdV hierarchy
The Toda field theories / 2.7:
The Kepler problem
Classical inverse scattering method / 13:
The Euler top / 14:
Symplectic geometry
Riemann surfaces / 2.9:
The Lagrange top
Lie algebras / 16:
Index
The Kowalevski top
The Neumann model / 2.11:
Geodesics on an ellipsoid / 2.12:
Separation of variables in the Neumann model / 2.13:
Examples of Lax pairs with spectral parameter / 3.1:
The Zakharov-Shabat construction / 3.2:
Coadjoint orbits and Hamiltonian formalism / 3.3:
Elementary flows and wave function / 3.4:
Factorization problem / 3.5:
Tau-functions / 3.6:
Integrable field theories and monodromy matrix / 3.7:
Abelianization / 3.8:
Poisson brackets of the monodromy matrix / 3.9:
The group of dressing transformations / 3.10:
Soliton solutions / 3.11:
The classical and modified Yang-Baxter equations / 4.1:
Algebraic meaning of the classical Yang-Baxter equations / 4.2:
Adler-Kostant-Symes scheme / 4.3:
Construction of integrable systems / 4.4:
Solving by factorization / 4.5:
The open Toda chain / 4.6:
The r-matrix of the Toda models / 4.7:
Solution of the open Toda chain / 4.8:
Toda system and Hamiltonian reduction / 4.9:
The Lax pair of the Kowalevski top / 4.10:
The spectral curve / 5.1:
The eigenvector bundle / 5.2:
The adjoint linear system / 5.3:
Time evolution / 5.4:
Theta-functions formulae / 5.5:
Baker-Akhiezer functions / 5.6:
Linearization and the factorization problem / 5.7:
Symplectic form / 5.8:
Separation of variables and the spectral curve / 5.10:
Riemann surfaces and integrability / 5.11:
Infinite-dimensional systems / 5.13:
The model / 6.1:
The eigenvectors / 6.2:
Reconstruction formula / 6.4:
Symplectic structure / 6.5:
The Sklyanin approach / 6.6:
The Poisson brackets / 6.7:
Reality conditions / 6.8:
The spin Calogero-Moser model / 7.1:
Lax pair / 7.2:
The r-matrix / 7.3:
The scalar Calogero-Moser model / 7.4:
Reconstruction formulae / 7.5:
Poles systems and double-Bloch condition / 7.9:
Hitchin systems / 7.11:
Examples of Hitchin systems / 7.12:
The trigonometric Calogero-Moser model / 7.13:
Monodromy data / 8.1:
Isomonodromy and the Riemann-Hilbert problem / 8.3:
Schlesinger transformations / 8.4:
Ricatti equation / 8.6:
Sato's formula / 8.8:
The Hirota equations / 8.9:
Tau-functions and theta-functions / 8.10:
The Painleve equations / 8.11:
Fermions and GL [infinity] / 9.1:
Boson-fermion correspondence / 9.3:
Tau-functions and Hirota bilinear identities / 9.4:
The KP hierarchy and its soliton solutions / 9.5:
Fermions and Grassmannians / 9.6:
Schur polynomials / 9.7:
From fermions to pseudo-differential operators / 9.8:
The Segal-Wilson approach / 9.9:
The algebra of pseudo-differential operators / 10.1:
The Baker-Akhiezer function of KP / 10.2:
Algebro-geometric solutions of KP / 10.4:
The tau-function of KP / 10.5:
The generalized KdV equations / 10.6:
KdV Hamiltonian structures / 10.7:
Bihamiltonian structure / 10.8:
The Drinfeld-Sokolov reduction / 10.9:
Whitham equations / 10.10:
Solution of the Whitham equations / 10.11:
The KdV equation / 11.1:
Hamiltonian structures and Virasoro algebra / 11.2:
Algebro-geometric solutions / 11.4:
Finite-zone solutions / 11.6:
Analytical description of solitons / 11.7:
Local fields / 11.9:
Whitham's equations / 11.10:
The Liouville equation / 12.1:
The Toda systems and their zero-curvature representations / 12.2:
Solution of the Toda field equations / 12.3:
Hamiltonian formalism / 12.4:
Conformal structure / 12.5:
Dressing transformations / 12.6:
The affine sinh-Gordon model / 12.7:
Dressing transformations and soliton solutions / 12.8:
N-soliton dynamics / 12.9:
The sine-Gordon equation / 12.10:
The Jost solutions / 13.2:
Inverse scattering as a Riemann-Hilbert problem / 13.3:
Time evolution of the scattering data / 13.4:
The Gelfand-Levitan-Marchenko equation / 13.5:
Poisson brackets of the scattering data / 13.6:
Poisson manifolds and symplectic manifolds / 13.8:
Coadjoint orbits / 14.2:
Symmetries and Hamiltonian reduction / 14.3:
The case M = T*G / 14.4:
Poisson-Lie groups / 14.5:
Action of a Poisson-Lie group on a symplectic manifold / 14.6:
The groups G and G* / 14.7:
Smooth algebraic curves / 14.8:
Hyperelliptic curves / 15.2:
The Riemann-Hurwitz formula / 15.3:
The field of meromorphic functions of a Riemann surface / 15.4:
Line bundles on a Riemann surface / 15.5:
Divisors / 15.6:
Chern class / 15.7:
Serre duality / 15.8:
The Riemann-Roch theorem / 15.9:
Abelian differentials / 15.10:
Riemann bilinear identities / 15.11:
Jacobi variety / 15.12:
Theta-functions / 15.13:
The genus 1 case / 15.14:
The Riemann-Hilbert factorization problem / 15.15:
Lie groups and Lie algebras / 16.1:
Semi-simple Lie algebras / 16.2:
Linear representations / 16.3:
Real Lie algebras / 16.4:
Affine Kac-Moody algebras / 16.5:
Vertex operator representations / 16.6:
Introduction / 1:
Integrable dynamical systems / 2:
Synopsis of integrable systems / 2.1:
7.

図書

図書
Youssef Jabri
出版情報: Cambridge : Cambridge University Press, 2003  xii, 369 p. ; 24 cm
シリーズ名: Encyclopedia of mathematics and its applications / edited by G.-C. Rota ; 95
所蔵情報: loading…
目次情報: 続きを見る
Retrospective / 1:
First Steps toward the Mountains / Part I:
Palais-Smale condition. Definitions and examples / 2:
Variational principle / 3:
Deformation lemma / 4:
Reaching the Mountain Pass through Easy Climbs / Part II:
The finite dimensional MPT / 5:
The topological MPT / 6:
The classical MPT / 7:
The multidimensional MPT / 8:
A Deeper Insight in Mountain Topology / Part III:
The limiting case in the MPT / 9:
Palais-Smale condition versus asymptotic behavior / 10:
Symmetry and the MPT / 11:
The structure of the critical set in the MPT / 12:
Weighted Palais-Smale conditions / 13:
The Landscape Becoming Less Smooth / Part IV:
The semismooth MPT / 14:
The nonsmooth MPT / 15:
The metric MPT / 16:
Speculating about the Mountain Pass Geometry / Part V:
The MPT on convex domains / 17:
A MPT in order intervals / 18:
The linking principle / 19:
The intrinsic MPT / 20:
Geometrically contrained MPT / 21:
Technical Climbs / Part VI:
Numerical MPT implementations / 22:
Perturbation from symmetry and the MPT / 23:
Applying the MPT in bifurcation problems / 24:
More climbs / 25:
Background material / Appendix A:
Retrospective / 1:
First Steps toward the Mountains / Part I:
Palais-Smale condition. Definitions and examples / 2:
8.

図書

図書
by Radu Miron
出版情報: Dordrecht : Kluwer Academic, c2003  xvi, 247 p. ; 24 cm
シリーズ名: Fundamental theories of physics ; v. 132
所蔵情報: loading…
9.

図書

図書
Alberto Abbondandolo
出版情報: Boca Raton : Chapman & Hall/CRC, c2001  xi, 189 p. ; 24 cm
シリーズ名: Research notes in mathematics ; 425
所蔵情報: loading…
10.

図書

図書
Pol Vanhaecke
出版情報: Berlin : Springer, c2001  x, 256 p. ; 24 cm
シリーズ名: Lecture notes in mathematics ; 1638
所蔵情報: loading…
文献の複写および貸借の依頼を行う
 文献複写・貸借依頼