Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium
Massimiliano Berti; Philippe Bolle
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1998)
- Volume: 27, Issue: 2, page 331-377
- ISSN: 0391-173X
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top- [1] A. Ambrosetti - M. Badiale, Homoclinics: Poincaré-Melnikov type results via a variational approach, C.R.Acad.Sci. Paris Sér. I-Math323 (1996), 753-758; Ann. Inst. H. Poincaré Anal. Non Linéaire15 (1998), 233-252. Zbl1004.37043MR1416171
- [2] H. Amann, A note on degree theory for gradient mappings, Proc. Amer. Math. Soc.84 (1982), 591-595. Zbl0501.58012MR660610
- [3] M. Berti - P. Bolle, Homoclinics and chaotic behaviour for perturbed second order systems, to appear in Ann. Mat. Pura Appl. Zbl0957.37019MR1746547
- [4] M. Berti - P. Bolle, Variational Construction of homoclinics and chaos in presence of a saddle-saddle equilibrium, Rend. Mat. Acc. Lincei9 (1998), 167-175. Zbl0921.58023MR1683007
- [5] S. Bolotin - P. Rabinowitz, A variational construction of chaotic trajectories for a Hamiltonian system on a torus, Boll. Un. Mat. Ital. 1-B8 (1998), 541-570. Zbl0957.70020MR1662325
- [6] B. Buffoni - E. Séré, A global condition for quasi-random behavior in a class of conservative systems, Comm. Pure Appl. Math.49 (1966), 285-305. Zbl0860.58027MR1374173
- [7] B. Buffoni - E. Séré, Chaotic dynamics in natural Lagrangian systems: a variational approach, preprint. Zbl0860.58027
- [8] R. Devaney, Homoclinic orbits in Hamiltonian systems, J. Differential Equations21 (1976), 431-438. Zbl0343.58005MR442990
- [9] R. Devaney, Transversal homoclinic orbits in an integrable Hamiltonian systems, Amer. J. Math.100 (1978), 631-642. Zbl0406.58019MR494258
- [10] H. Hofer, A note on the topological degree at a critical point of mountain-pass type, Proc. Amer. Math. Soc.90 (1984), 309-315. Zbl0545.58015MR727256
- [11] P.J. Holmes, Periodic, non-periodic and irregular motions in a Hamiltonian system, Rocky Mountain J. Math10 (1980), 679-693. Zbl0427.70026MR595097
- [12] E. Séré, Looking for the Bernoulli shift, Ann. Inst. H. Poincaré Anal. Non Linéaire10 (1993), 561-590. Zbl0803.58013MR1249107
- [13] D.V. Turaev - L.P. Shil'nikov, On Hamiltonian systems with homoclinic curves of a saddle, Dokl. Akad. Nauk UzSSR304 (1989), 811-814. Zbl0689.58013MR988994
- [14] S. Wiggins, "Global Bifurcation and Chaos", Applied Mathematical Sciences, Vol.73, Springer-Verlag, 1988. Zbl0661.58001MR956468