Àlex Haro 1999 Nonlinearity 12 1299 doi:10.1088/0951-7715/12/5/306
Àlex Haro
Show affiliationsRecommended by A I Neishtadt
We apply variational methods to converse KAM theory. These are useful for symplectomorphisms in the annulus that satisfy weaker hypotheses than those usually required. For instance, we do not need the existence of a global Lagrangian generating function. We obtain the variational principles from the primitive function of our symplectomorphism. They are introduced not only for the orbits of a symplectomorphism, but also for the so-called invariant Lagrangian graphs (ILG). Among the non-degenerate ILG we focus on the minimizing ones. Applications are also described for a broad class of examples.
70H30 Other variational principles
37J40 Perturbations, normal forms, small divisors, KAM theory, Arnol'd diffusion
Issue 5 (September 1999)
Received 26 October 1998
Àlex Haro 1999 Nonlinearity 12 1299
C Markakis et al 2009 J. Phys.: Conf. Ser. 189 012024
John D Steele 2002 Class. Quantum Grav. 19 259
F A Gianturco and T Stoecklin 2001 J. Phys. B: At. Mol. Opt. Phys. 34 1695
Thomas H Court and Moritz von Rohr 1930 Trans. Opt. Soc. 32 113
Jan Ambjørn et al JHEP05(2000)023
A Balsamo et al 2006 Metrologia 43 396
Michel Brissaud 2006 J. Micromech. Microeng. 16 875
Zhao-hua Cheng et al 1995 J. Phys.: Condens. Matter 7 4707
L Cerruti 1994 Metrologia 31 159