@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}, volume = {17}, year = {2000}, pages = {673-709}, mrnumber = {1804651}, zbl = {0978.37024}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2000__17_6_673_0} }
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) pp. 673-709. http://gdmltest.u-ga.fr/item/AIHPC_2000__17_6_673_0/
[1] Complex dynamics in a class of reversible equations, in: Proc. of Autumn School on Nonlinear Analysis and Differential Equations, Lisbon, 1998, to appear. | MR 1800617 | Zbl 0994.34029
, , ,[2] Ordinary Differential Equations, De Gruyter, Berlin, 1990. | MR 1071170 | Zbl 0708.34002
,[3] Homoclinics: Poincaré-Melnikov type results via a variational approach, Ann. IHP, Anal. non Lin. 15 (1998) 233-252. | Numdam | MR 1614571 | Zbl 1004.37043
, ,[4] Mather sets for twist maps and geodesics on tori, in: Dinamics Reported, Vol.1, Teubner, 1988, pp. 1-56. | MR 945963 | Zbl 0664.53021
,[5] The existence of homoclinic motions, Vest. Mosk. Univ., Matem. 38 (1983) 98-103. | MR 728558 | Zbl 0549.58019
,[6] A variational construction of chaotic trajectories for a Hamiltonian system on a torus, Boll. UMI.1 (1998) 541-570. | MR 1662325 | Zbl 0957.70020
, ,[7] A global condition for quasi-random behavior in a class of conservative systems, Comm. Pure Appl. Math. 49 (1996) 285-305. | MR 1374173 | Zbl 0860.58027
, ,[8] Homoclinic solutions to periodic motions in a class of reversible equations, Calc. Var. and PDEs. 9 (1999) 157-184. | MR 1714117 | Zbl 0967.34041
, ,[9] A variational approach to homoclinic orbits in Hamiltonian systems, Math. Annalen 288 (1990) 133-160. | MR 1070929 | Zbl 0731.34050
, , ,[10] Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. AMS 4 (1991) 693-727. | MR 1119200 | Zbl 0744.34045
, ,[11] Multibump periodic solutions for a family of Hamiltonian systems, Topol. Methods in Nonlinear Anal. 4 (1995) 31-57. | MR 1321808 | Zbl 0819.34028
, ,[12] Variational construction of connecting orbits, Ann. Inst. Fourier 43 (1993)1349-1386. | Numdam | MR 1275203 | Zbl 0803.58019
,[13] Heteroclinic chains for a reversible Hamiltonian system, Nonlin. Anal. TMA 28 (1997) 871-887. | MR 1422191 | Zbl 0870.34050
,[14] A global condition for periodic Duffing-like equations, Trans. AMS 351 (1999) 3713-3724. | MR 1487629 | Zbl 0926.37005
, , ,[15] Homoclinic orbits in the forced pendulum system, Fields Inst. Comm. 8 (1996) 113-126. | MR 1383843 | Zbl 0851.34048
, ,[16] Heteroclinics for a reversible Hamiltonian system, Ergodic Theory Dynamical Systems 14 (1994) 817-829. | MR 1304144 | Zbl 0818.34025
,[17] Heteroclinics for a reversible Hamiltonian system, 2, Differential Integral Equations 7 (1994) 1557-1572. | MR 1269671 | Zbl 0835.34050
,[18] Connecting orbits for a reversible Hamiltonian system, Ergodic Theory Dynamical Systems, to appear. | MR 1804957 | Zbl 0981.37020
,[19] Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Zeit. 209 (1992) 27-42. | MR 1143210 | Zbl 0725.58017
,[20] Looking for the Bernoulli shift, Ann. IHP, Anal. non Lin. 10 (1993) 561- 590. | Numdam | MR 1249107 | Zbl 0803.58013
,[21] On the structure of the solution set of forced pendulum-type equations, J. Differential Equations 131 (1996) 189-208. | MR 1419011 | Zbl 0864.34038
, , ,[22] Nondegeneracy and chaotic motions for a class of almost-periodic Lagrangian systems, Nonlin. Anal. TMA 37 (1999) 337-361. | MR 1694395 | Zbl 0948.37022
,[23] Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer Verlag, New York, 1990. | MR 1056699 | Zbl 0701.58001
,