Yiming Long

Index Theory for Symplectic Paths with Applications (eBook, PDF)

• Format: PDF

Produktbeschreibung

This book gives an introduction to index theory for symplectic matrix paths and its iteration theory, as well as applications to periodic solution problems of nonlinear Hamiltonian systems. The applications of these concepts yield new approaches to some outstanding problems. Particular attention is given to the minimal period solution problem of Hamiltonian systems and the existence of infinitely many periodic points of the Poincaré map of Lagrangian systems on tori.

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Produktdetails

• Verlag: Springer Basel
• Seitenzahl: 380
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783034881753
• Artikelnr.: 53147310

Autorenporträt

Long, Y., Nankai University, Tianjin, People's Republic of China

Inhaltsangabe

I The Symplectic Group Sp(2n).- 1 Algebraic Aspects.- 2 Topological Aspects.- II The Variational Method.- 3 Hamiltonian Systems and Canonical Transformations.- 4 The Variational Functional.- III Index Theory.- 5 Index Functions for Symplectic Paths.- 6 Properties of Index Functions.- 7 Relations with other Morse Indices.- IV Iteration Theory.- 8 Precise Iteration Formulae.- 9 Bott-type Iteration Formulae.- 10 Iteration Inequalities.- 11 The Common Index Jump Theorem.- 12 Index Iteration Theory for Closed Geodesics.- V Applications.- 13 The Rabinowitz Conjecture.- 14 Periodic Lagrangian Orbits on Tori.- 15 Closed Characteristics on Convex Hypersurfaces.