Geometric description of chaos in two-degrees-of-freedom Hamiltonian systems

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 53, Issue 1, 1996, Pages 179-188

  Cerruti Sola, Monica ^a,b   Pettini, Marco ^a,b  

^a INAF OSSERVATORIO ASTROFISICO DI ARCETRI   (Italy)

^b INFN SEZIONE DI FIRENZE   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000042390     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.53.179     Document Type: Article

References (15)

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13. Precisely, a positive measure of points where K(2)< 0 could be not sufficient to make unstable the solutions of Eq. (31). In fact it is well known that a reversed pendulum can be stabilized by a sufficiently rapidly varying force term. This is described by the equation x dotdot + ( ω2+- d2) x =0, where ω2+- d2 is alternatively positive and negative [see V. I. Arnold, Les Méthodes Mathématiques de la Méchanique Classique (MIR, Moscow, 1976)]. In any case this is a very special exception.
14. L. P. Eisenhart, Ann. Math. 30, 591 (1929).
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