Homoclinic and period-doubling bifurcations for damped systems

Ugo Bessi

Annales de l'I.H.P. Analyse non linéaire (1995)

  • Volume: 12, Issue: 1, page 1-25
  • ISSN: 0294-1449

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Bessi, Ugo. "Homoclinic and period-doubling bifurcations for damped systems." Annales de l'I.H.P. Analyse non linéaire 12.1 (1995): 1-25. <http://eudml.org/doc/78350>.

@article{Bessi1995,
author = {Bessi, Ugo},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {damped systems; homoclinic bifurcations; infinite cascade of period- doubling bifurcations},
language = {eng},
number = {1},
pages = {1-25},
publisher = {Gauthier-Villars},
title = {Homoclinic and period-doubling bifurcations for damped systems},
url = {http://eudml.org/doc/78350},
volume = {12},
year = {1995},
}

TY - JOUR
AU - Bessi, Ugo
TI - Homoclinic and period-doubling bifurcations for damped systems
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1995
PB - Gauthier-Villars
VL - 12
IS - 1
SP - 1
EP - 25
LA - eng
KW - damped systems; homoclinic bifurcations; infinite cascade of period- doubling bifurcations
UR - http://eudml.org/doc/78350
ER -

References

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  2. [2] U. Bessi, A Variational Proof of a Sitnikov-like Theorem, to appear on Nonlin. Anal., T.M.A. Zbl0778.34036MR1220837
  3. [3] U. Bessi, Global Homoclinic Bifurcation for Damped Systems, to appear onMath. Zeit. Zbl0826.34041MR1324535
  4. [4] S.N. Chow, J.K. Hale and J. Mallet-Paret, An Example of Bifurcation to Homoclinic Orbits, J.D.E., Vol. 37, 1980, pp. 351-373. Zbl0439.34035MR589997
  5. [5] V. Coti Zelati, I. Ekeland and E. Séré, A Variational Approach to Homoclinic Orbits in Hamiltonian Systems, Math. Ann., Vol. 288, 1990, pp. 133-160. Zbl0731.34050MR1070929
  6. [6] V. Coti Zelati and P.H. Rabinowitz, Homoclinic Orbits for Second Order Hamiltonian Systems Possessing Superquadratic Potentials, J. Amer. Math. Soc., Vol. 4, 1991, pp. 693-727. Zbl0744.34045MR1119200
  7. [7] J. Franks, Period Doubling and the Lefschetz Formula, Trans. Am. Math. Soc., Vol. 1, 1985, pp. 275-283. Zbl0552.58025MR766219
  8. [8] J. Leray and J. Schauder, Topologie et Équations fonctionnelles, Ann. Scien. École norm. Sup., 1934, pp. 45-78. Zbl0009.07301MR1509338JFM60.0322.02
  9. [9] S. Mathlouthi, Bifurcation d'orbites homoclines pour les systèmes hamiltoniens, Annales de la Faculté des Sciences de Toulouse, Vol. 1, 1992, pp. 211-236. Zbl0780.58034MR1202072
  10. [10] A. Marino and G. Prodi, Metodi Perturbativi nella Teoria di Morse, Boll. U.M.I., Vol. 11, 1975, pp. 1-32. Zbl0311.58006MR418150
  11. [11] M. Misiurewitz, On Non-continuity of Topological Entropy, Bull. Acad. Pol. Sci. , Vol. 19, 1971, pp. 319-320. Zbl0208.52101MR287578
  12. [12] S. Newhouse, Lectures on Dynamical Systems, C.I.M.E. Summer School at Bressanone, Italy, Birkhaueser, Boston, 1980. Zbl0444.58001MR660646
  13. [13] P.H. Rabinowitz, Nonlinear Sturm-Liouville Problems for Second Order O.D.E., Comm. Pure and Appl. Math., Vol. 23, 1970, pp. 939-961. Zbl0206.09706MR284642
  14. [14] E. Séré, Looking for the Bernoulli Shift, Ann. Inst. H. Poincaré, Anal. non Linéaire, Vol. 10, 1993, pp. 561-590. Zbl0803.58013MR1249107

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