JournalscmhVol. 73, No. 4pp. 516–547

Minimal orbits close to periodic frequencies

  • U. Bessi

    Scuola Normale Superiore, Pisa, Italy
  • V. Semijopuva

    Scuola Normale Superiore, Pisa, Italy
Minimal orbits close to periodic frequencies cover

Abstract

Let L(Q,Q˙)=12Q˙2+h(Q,Q˙){\cal L}(Q,\dot Q)={1\over2}\vert\dot{Q}\vert^2+h(Q,\dot Q) with h analytic of small norm. The problem of Arnold's diffusion consists in finding conditions on h which guarantee the existence of orbits Q of L{\cal L} with Q˙\dot Q connecting two arbitrary points of frequency space. Recently, J. N. Mather has found a sufficient condition for Arnold's diffusion; this condition is not read on h itself, but on the set of all action-minimizing orbits of L{\cal L}. In this paper we try to characterize those action-minimizing orbits whose mean frequency is close to periodic.

Cite this article

U. Bessi, V. Semijopuva, Minimal orbits close to periodic frequencies. Comment. Math. Helv. 73 (1998), no. 4, pp. 516–547

DOI 10.1007/S000140050067