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Qualitative analysis of the anisotropic two-body problem with generalized Lennard-Jones potential

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Abstract

This paper continue the study of the generalized Lennard-Jones potential started in Bărbosu et al. (J Math Chem 49(9):1961–1975, 2011) for a more general situation. More precisely we study the two-body problem with generalized Lennard-Jones potential in an anisotropic space. We will show that the set of initial conditions leading to collisions and ejections have positive measure. We also study the capture and escape solutions in the zero-energy case using the infinity manifold. We also show that the flow on the zero energy manifold of a two-body problem given by the sum of the Newtonian potential and the two anisotropic perturbations corresponding to the generalized Lennard-Jones potential is chaotic.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, University of Oradea, University Street 1, 410087, Oradea, Romania

    Daniel Paşca

  2. Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001, Lisboa, Portugal

    Cláudia Valls

Authors
  1. Daniel Paşca
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  2. Cláudia Valls
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Correspondence to Daniel Paşca.

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Dedicated to Professor Jaume Llibre on the occasion of his 60th birthday with deep esteem and respect.

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Paşca, D., Valls, C. Qualitative analysis of the anisotropic two-body problem with generalized Lennard-Jones potential. J Math Chem 50, 2671–2688 (2012). https://doi.org/10.1007/s10910-012-0057-z

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  • DOI: https://doi.org/10.1007/s10910-012-0057-z

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