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On the Lyapunov instability in Newtonian dynamics

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Published 18 August 2021 • © 2021 IOP Publishing Ltd & London Mathematical Society
, , Citation J M Burgos et al 2021 Nonlinearity 34 6719 DOI 10.1088/1361-6544/ac1a1a

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Author e-mails

burgos@math.cinvestav.mx

eze@fing.edu.uy

miguel@cmat.edu.uy

Author affiliations

1 Departamento de Matemáticas, CINVESTAV–CONACYT, Av. Instituto Politécnico Nacional 2508, Col. San Pedro Zacatenco, 07360 Ciudad de México, Mexico

2 IMERL, Facultad de Ingeniería, Universidad de la República, Av. Herrera y Reissig 565, 11300 Montevideo, Uruguay

3 Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay

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4 Author to whom any correspondence should be addressed.

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Dates

  1. Received 25 July 2019
  2. Revised 14 July 2021
  3. Accepted 3 August 2021
  4. Published

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0951-7715/34/10/6719

Abstract

We prove Lyapunov instability for cases in which the local minimum of the potential energy is reached on a hypersurface of the configuration space. In contrast to the known results in this direction, which hold for potentials satisfying hypotheses on the first non-zero jet, this new result covers several real analytic cases that the previous do not.

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10.1088/1361-6544/ac1a1a