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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Berti, Massimiliano, and Bolle, Philippe. "Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 27.2 (1998): 331-377. <http://eudml.org/doc/84361>.

@article{Berti1998,
author = {Berti, Massimiliano, Bolle, Philippe},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {autonomous Lagrangian systems; chaotic dynamics; zero energy level; homoclinic orbits; multibump homoclinic solutions; topological entropy},
language = {eng},
number = {2},
pages = {331-377},
publisher = {Scuola normale superiore},
title = {Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium},
url = {http://eudml.org/doc/84361},
volume = {27},
year = {1998},
}

TY - JOUR
AU - Berti, Massimiliano
AU - Bolle, Philippe
TI - Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1998
PB - Scuola normale superiore
VL - 27
IS - 2
SP - 331
EP - 377
LA - eng
KW - autonomous Lagrangian systems; chaotic dynamics; zero energy level; homoclinic orbits; multibump homoclinic solutions; topological entropy
UR - http://eudml.org/doc/84361
ER -

References

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2. [2] H. Amann, A note on degree theory for gradient mappings, Proc. Amer. Math. Soc.84 (1982), 591-595. Zbl0501.58012MR660610
3. [3] M. Berti - P. Bolle, Homoclinics and chaotic behaviour for perturbed second order systems, to appear in Ann. Mat. Pura Appl. Zbl0957.37019MR1746547
4. [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. [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. [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. [7] B. Buffoni - E. Séré, Chaotic dynamics in natural Lagrangian systems: a variational approach, preprint. Zbl0860.58027
8. [8] R. Devaney, Homoclinic orbits in Hamiltonian systems, J. Differential Equations21 (1976), 431-438. Zbl0343.58005MR442990
9. [9] R. Devaney, Transversal homoclinic orbits in an integrable Hamiltonian systems, Amer. J. Math.100 (1978), 631-642. Zbl0406.58019MR494258
10. [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. [11] P.J. Holmes, Periodic, non-periodic and irregular motions in a Hamiltonian system, Rocky Mountain J. Math10 (1980), 679-693. Zbl0427.70026MR595097
12. [12] E. Séré, Looking for the Bernoulli shift, Ann. Inst. H. Poincaré Anal. Non Linéaire10 (1993), 561-590. Zbl0803.58013MR1249107
13. [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. [14] S. Wiggins, "Global Bifurcation and Chaos", Applied Mathematical Sciences, Vol.73, Springer-Verlag, 1988. Zbl0661.58001MR956468

Citations in EuDML Documents

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1. Massimiliano Berti, Philippe Bolle, Diffusion time and splitting of separatrices for nearly integrable isochronous Hamiltonian systems
2. Massimiliano Berti, Philippe Bolle, A functional analysis approach to Arnold diffusion

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