(Quasi)periodic solutions in (in)finite dimensional Hamiltonian systems with applications to celestial mechanics and wave equation

DOI10.4171/PM/1820zbMath1151.37324OpenAlexW1982774180MaRDI QIDQ959456

Enrico Valdinoci, Luca Biasco

Publication date: 11 December 2008

Published in: Portugaliae Mathematica. Nova Série (Search for Journal in Brave)

Full work available at URL: http://www.ems-ph.org/journals/show_pdf.php?issn=0032-5155&vol=65&iss=4&rank=1

zbMATH Keywords

wave equation\(N\)-body problemnearly-integrable Hamiltonian systemsperiodic solutions lower-dimensional elliptic tori

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Wave equation (35L05) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) (n)-body problems (70F10) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27) Bifurcation problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K50)

Related Items

A Birkhoff-Lewis type theorem for the nonlinear wave equation ⋮ Periodic orbits accumulating onto elliptic tori for the \((N + 1)\)-body problem

Cites Work

• Elliptic two-dimensional invariant tori for the planetary three-body problem
• Periodic solutions of nonlinear wave equations with general nonlinearities
• Nonlinear oscillations of Hamiltonian PDEs
• Cantor families of periodic solutions for completely resonant nonlinear wave equations
• A Birkhoff--Lewis-Type Theorem for Some Hamiltonian PDEs
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS
• Families of periodic solutions of resonant PDEs
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