Isolated periodic minima are unstable

Antonio J. Ureña

Annales de l'I.H.P. Analyse non linéaire (2006)

  • Volume: 23, Issue: 6, page 877-889
  • ISSN: 0294-1449

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Ureña, Antonio J.. "Isolated periodic minima are unstable." Annales de l'I.H.P. Analyse non linéaire 23.6 (2006): 877-889. <http://eudml.org/doc/78718>.

@article{Ureña2006,
author = {Ureña, Antonio J.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {instability; periodic minimizers; parabolic case},
language = {eng},
number = {6},
pages = {877-889},
publisher = {Elsevier},
title = {Isolated periodic minima are unstable},
url = {http://eudml.org/doc/78718},
volume = {23},
year = {2006},
}

TY - JOUR
AU - Ureña, Antonio J.
TI - Isolated periodic minima are unstable
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2006
PB - Elsevier
VL - 23
IS - 6
SP - 877
EP - 889
LA - eng
KW - instability; periodic minimizers; parabolic case
UR - http://eudml.org/doc/78718
ER -

References

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  1. [1] Carathéodory C., Calculus of Variations and Partial Differential Equations of the First Order, Chelsea, New York, 1989. Zbl0505.49001
  2. [2] Dancer E.N., Ortega R., The index of Lyapunov stable fixed points in two dimensions, J. Dynam. Differential Equations6 (4) (1994) 631-637. Zbl0811.34018MR1303278
  3. [3] Hartman P., Ordinary Differential Equations, Birkhäuser, Boston, 1982. Zbl0476.34002MR658490
  4. [4] Moser J., Selected Chapters in the Calculus of Variations. Lecture Notes by Oliver Knill, Lectures in Mathematics ETH Zürich, Birkhäuser, Basel, 2003. Zbl1045.37001MR1988457
  5. [5] Offin D., Hyperbolic minimizing geodesics, Trans. Amer. Math. Soc.352 (7) (2000) 3323-3338. Zbl0956.37019MR1661274
  6. [6] Offin D., Skoczylas W., Instability of periodic orbits in the restricted three body problem, in: New Advances in Celestial Mechanics and Hamiltonian Systems, Kluwer/Plenum, New York, 2004, pp. 153-168. MR2083011
  7. [7] Ortega R., The number of stable periodic solutions of time-dependent Hamiltonian systems with one degree of freedom, Ergodic Theory Dynam. Systems18 (4) (1998) 1007-1018. Zbl0946.34036MR1645346
  8. [8] Ortega R., Instability of periodic solutions obtained by minimization, in: The First 60 Years of Nonlinear Analysis of Jean Mawhin, World Scientific, 2004, pp. 189-197. Zbl1210.37042MR2128887
  9. [9] Siegel C.L., Moser J., Lectures on Celestial Mechanics, Translation by Charles I. Kalme, Die Grundlehren der mathematischen Wissenschaften, Band 187, Springer-Verlag, New York, 1971. Zbl0312.70017MR502448

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