The flow of classical mechanical cubic potential systems

Manuel Falconi; E. A. Lacomba; C. Vidal

doi:10.3934/dcds.2004.11.827

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2004, Volume 11, Issue 4: 827-842. Doi: 10.3934/dcds.2004.11.827

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The flow of classical mechanical cubic potential systems

1.
Department of Mathematics, Facultad de Ciencias, UNAM, Ciudad Universitaria, México, D.F. 04510
2.
Department of Mathematics, UAM-I, P.O.Box 55-534, México, D.F. 09340, MEX
3.
Department of Mathematics, Universidade Federal de Pernambuco, Cidade Universitaria, Recife-Pe

Received: February 2003

Revised: January 2004

Published: October 2004

Abstract / Introduction Related Papers Cited by

Abstract

This paper describes the global flow of homogeneous polynomial potentials of degree 3 for negative and positive energy. For the negative energy case a blow up of McGehee type is enough to get the complete picture of the flow. In the positive energy case, McGehee blow up fails to give global information about the flow, but comparing with a separable case we are able to obtain all the possible asymptotic behavior of solutions, whenever the coefficients of the normal form of the potential are positive.

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Mathematics Subject Classification: 70F05, 70H05, 74G55, 37J99.

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