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October  2004, 11(4): 827-842. doi: 10.3934/dcds.2004.11.827

The flow of classical mechanical cubic potential systems

Manuel Falconi 1, , E. A. Lacomba 2, and  C. Vidal 3,

1. 

Department of Mathematics, Facultad de Ciencias, UNAM, Ciudad Universitaria, México, D.F. 04510, Mexico
2. 

Department of Mathematics, UAM-I, P.O.Box 55-534, México, D.F. 09340, MEX, Mexico
3. 

Department of Mathematics, Universidade Federal de Pernambuco, Cidade Universitaria, Recife-Pe, Brazil

Received  February 2003 Revised  January 2004 Published  September 2004

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.
Keywords: Hamiltonian systems, homogeneous polynomial potentials, global flow..
Mathematics Subject Classification: 70F05, 70H05, 74G55, 37J9.
Citation: Manuel Falconi, E. A. Lacomba, C. Vidal. The flow of classical mechanical cubic potential systems. Discrete & Continuous Dynamical Systems, 2004, 11 (4) : 827-842. doi: 10.3934/dcds.2004.11.827
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