Geodesic
Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 3, pp. 167-175

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

We consider autonomous Lagrangian systems possessing two homoclinic orbits to an hyperbolic equilibrium of saddle-saddle type with two different characteristic exponents. Under a nondegeneracy assumption on the homoclinics and under suitable conditions on the geometric behaviour of these homoclinics near the equilibrium we show, by variational methods, that they give rise to an infinite family of multibump homoclinic solutions. We relax the nondegeneracy assumption when the two characteristic exponents are close one to the other. 
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     title = {Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {167--175},
     publisher = {mathdoc},
     volume = {Ser. 9, 9},
     number = {3},
     year = {1998},
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     mrnumber = {MR1683007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_3_a3/}
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Berti, Massimiliano; Bolle, Philippe. Variational construction of homoclinics and chaos in presence of a saddle-saddle equilibrium. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 3, pp. 167-175. http://geodesic.mathdoc.fr/item/RLIN_1998_9_9_3_a3/