Isolated periodic minima are unstable
Annales de l'I.H.P. Analyse non linéaire, Volume 23 (2006) no. 6, p. 877-889
@article{AIHPC_2006__23_6_877_0,
     author = {Ure\~na, Antonio J.},
     title = {Isolated periodic minima are unstable},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {23},
     number = {6},
     year = {2006},
     pages = {877-889},
     doi = {10.1016/j.anihpc.2005.09.010},
     zbl = {05138724},
     mrnumber = {2271699},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2006__23_6_877_0}
}
Ureña, Antonio J. Isolated periodic minima are unstable. Annales de l'I.H.P. Analyse non linéaire, Volume 23 (2006) no. 6, pp. 877-889. doi : 10.1016/j.anihpc.2005.09.010. http://www.numdam.org/item/AIHPC_2006__23_6_877_0/

[1] Carathéodory C., Calculus of Variations and Partial Differential Equations of the First Order, Chelsea, New York, 1989. | Zbl 0505.49001

[2] Dancer E.N., Ortega R., The index of Lyapunov stable fixed points in two dimensions, J. Dynam. Differential Equations 6 (4) (1994) 631-637. | MR 1303278 | Zbl 0811.34018

[3] Hartman P., Ordinary Differential Equations, Birkhäuser, Boston, 1982. | MR 658490 | Zbl 0476.34002

[4] Moser J., Selected Chapters in the Calculus of Variations. Lecture Notes by Oliver Knill, Lectures in Mathematics ETH Zürich, Birkhäuser, Basel, 2003. | MR 1988457 | Zbl 1045.37001

[5] Offin D., Hyperbolic minimizing geodesics, Trans. Amer. Math. Soc. 352 (7) (2000) 3323-3338. | MR 1661274 | Zbl 0956.37019

[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. | MR 2083011

[7] Ortega R., The number of stable periodic solutions of time-dependent Hamiltonian systems with one degree of freedom, Ergodic Theory Dynam. Systems 18 (4) (1998) 1007-1018. | MR 1645346 | Zbl 0946.34036

[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. | MR 2128887 | Zbl 02226496

[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. | MR 502448 | Zbl 0312.70017