A variational approach to chaotic dynamics in periodically forced nonlinear oscillators
Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 6, pp. 673-709. 
@article{AIHPC_2000__17_6_673_0,
     author = {Bosetto, Elena and Serra, Enrico},
     title = {A variational approach to chaotic dynamics in periodically forced nonlinear oscillators},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {673--709},
     publisher = {Gauthier-Villars},
     volume = {17},
     number = {6},
     year = {2000},
     mrnumber = {1804651},
     zbl = {0978.37024},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2000__17_6_673_0/}
}
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Bosetto, Elena; Serra, Enrico. A variational approach to chaotic dynamics in periodically forced nonlinear oscillators. Annales de l'I.H.P. Analyse non linéaire, Tome 17 (2000) no. 6, pp. 673-709. http://www.numdam.org/item/AIHPC_2000__17_6_673_0/

[1] Alessio F., Calanchi M., Serra E., Complex dynamics in a class of reversible equations, in: Proc. of Autumn School on Nonlinear Analysis and Differential Equations, Lisbon, 1998, to appear. | MR | Zbl

[2] Amann H., Ordinary Differential Equations, De Gruyter, Berlin, 1990. | MR | Zbl

[3] Ambrosetti A., Badiale M., Homoclinics: Poincaré-Melnikov type results via a variational approach, Ann. IHP, Anal. non Lin. 15 (1998) 233-252. | Numdam | MR | Zbl

[4] Bangert V., Mather sets for twist maps and geodesics on tori, in: Dinamics Reported, Vol.1, Teubner, 1988, pp. 1-56. | MR | Zbl

[5] Bolotin S.V., The existence of homoclinic motions, Vest. Mosk. Univ., Matem. 38 (1983) 98-103. | MR | Zbl

[6] Bolotin S.V., Rabinowitz P.H., A variational construction of chaotic trajectories for a Hamiltonian system on a torus, Boll. UMI.1 (1998) 541-570. | MR | Zbl

[7] Buffoni B., Séré E., A global condition for quasi-random behavior in a class of conservative systems, Comm. Pure Appl. Math. 49 (1996) 285-305. | MR | Zbl

[8] Calanchi M., Serra E., Homoclinic solutions to periodic motions in a class of reversible equations, Calc. Var. and PDEs. 9 (1999) 157-184. | MR | Zbl

[9] Coti Zelati V., Ekeland I., Séré E., A variational approach to homoclinic orbits in Hamiltonian systems, Math. Annalen 288 (1990) 133-160. | MR | Zbl

[10] Coti Zelati V., Rabinowitz P.H., Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. AMS 4 (1991) 693-727. | MR | Zbl

[11] Coti Zelati V., Rabinowitz P.H., Multibump periodic solutions for a family of Hamiltonian systems, Topol. Methods in Nonlinear Anal. 4 (1995) 31-57. | MR | Zbl

[12] Mather J.N., Variational construction of connecting orbits, Ann. Inst. Fourier 43 (1993)1349-1386. | Numdam | MR | Zbl

[13] Maxwell T.O., Heteroclinic chains for a reversible Hamiltonian system, Nonlin. Anal. TMA 28 (1997) 871-887. | MR | Zbl

[14] Montecchiari P., Nolasco M., Terracini S., A global condition for periodic Duffing-like equations, Trans. AMS 351 (1999) 3713-3724. | MR | Zbl

[15] Offin D.C., Yu H.-F., Homoclinic orbits in the forced pendulum system, Fields Inst. Comm. 8 (1996) 113-126. | MR | Zbl

[16] Rabinowitz P.H., Heteroclinics for a reversible Hamiltonian system, Ergodic Theory Dynamical Systems 14 (1994) 817-829. | MR | Zbl

[17] Rabinowitz P.H., Heteroclinics for a reversible Hamiltonian system, 2, Differential Integral Equations 7 (1994) 1557-1572. | MR | Zbl

[18] Rabinowitz P.H., Connecting orbits for a reversible Hamiltonian system, Ergodic Theory Dynamical Systems, to appear. | MR | Zbl

[19] Séré E., Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Zeit. 209 (1992) 27-42. | MR | Zbl

[20] Séré E., Looking for the Bernoulli shift, Ann. IHP, Anal. non Lin. 10 (1993) 561- 590. | Numdam | MR | Zbl

[21] Serra E., Tarallo M., Terracini S., On the structure of the solution set of forced pendulum-type equations, J. Differential Equations 131 (1996) 189-208. | MR | Zbl

[22] Terracini S., Nondegeneracy and chaotic motions for a class of almost-periodic Lagrangian systems, Nonlin. Anal. TMA 37 (1999) 337-361. | MR | Zbl

[23] Wiggins S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer Verlag, New York, 1990. | MR | Zbl