A variational approach to chaotic dynamics in periodically forced nonlinear oscillators
Annales de l'I.H.P. Analyse non linéaire (2000)
- Volume: 17, Issue: 6, page 673-709
- ISSN: 0294-1449
Access Full Article
topHow to cite
topReferences
top- [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. Zbl0994.34029MR1800617
- [2] Amann H., Ordinary Differential Equations, De Gruyter, Berlin, 1990. Zbl0708.34002MR1071170
- [3] Ambrosetti A., Badiale M., Homoclinics: Poincaré-Melnikov type results via a variational approach, Ann. IHP, Anal. non Lin.15 (1998) 233-252. Zbl1004.37043MR1614571
- [4] Bangert V., Mather sets for twist maps and geodesics on tori, in: Dinamics Reported, Vol.1, Teubner, 1988, pp. 1-56. Zbl0664.53021MR945963
- [5] Bolotin S.V., The existence of homoclinic motions, Vest. Mosk. Univ., Matem.38 (1983) 98-103. Zbl0549.58019MR728558
- [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. Zbl0957.70020MR1662325
- [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. Zbl0860.58027MR1374173
- [8] Calanchi M., Serra E., Homoclinic solutions to periodic motions in a class of reversible equations, Calc. Var. and PDEs.9 (1999) 157-184. Zbl0967.34041MR1714117
- [9] Coti Zelati V., Ekeland I., Séré E., A variational approach to homoclinic orbits in Hamiltonian systems, Math. Annalen288 (1990) 133-160. Zbl0731.34050MR1070929
- [10] Coti Zelati V., Rabinowitz P.H., Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. AMS4 (1991) 693-727. Zbl0744.34045MR1119200
- [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. Zbl0819.34028MR1321808
- [12] Mather J.N., Variational construction of connecting orbits, Ann. Inst. Fourier43 (1993)1349-1386. Zbl0803.58019MR1275203
- [13] Maxwell T.O., Heteroclinic chains for a reversible Hamiltonian system, Nonlin. Anal. TMA28 (1997) 871-887. Zbl0870.34050MR1422191
- [14] Montecchiari P., Nolasco M., Terracini S., A global condition for periodic Duffing-like equations, Trans. AMS351 (1999) 3713-3724. Zbl0926.37005MR1487629
- [15] Offin D.C., Yu H.-F., Homoclinic orbits in the forced pendulum system, Fields Inst. Comm.8 (1996) 113-126. Zbl0851.34048MR1383843
- [16] Rabinowitz P.H., Heteroclinics for a reversible Hamiltonian system, Ergodic Theory Dynamical Systems14 (1994) 817-829. Zbl0818.34025MR1304144
- [17] Rabinowitz P.H., Heteroclinics for a reversible Hamiltonian system, 2, Differential Integral Equations7 (1994) 1557-1572. Zbl0835.34050MR1269671
- [18] Rabinowitz P.H., Connecting orbits for a reversible Hamiltonian system, Ergodic Theory Dynamical Systems, to appear. Zbl0981.37020MR1804957
- [19] Séré E., Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Zeit.209 (1992) 27-42. Zbl0725.58017MR1143210
- [20] Séré E., Looking for the Bernoulli shift, Ann. IHP, Anal. non Lin.10 (1993) 561- 590. Zbl0803.58013MR1249107
- [21] Serra E., Tarallo M., Terracini S., On the structure of the solution set of forced pendulum-type equations, J. Differential Equations131 (1996) 189-208. Zbl0864.34038MR1419011
- [22] Terracini S., Nondegeneracy and chaotic motions for a class of almost-periodic Lagrangian systems, Nonlin. Anal. TMA37 (1999) 337-361. Zbl0948.37022MR1694395
- [23] Wiggins S., Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer Verlag, New York, 1990. Zbl0701.58001MR1056699