@incollection{AST_2003__286__151_0,
author = {Bernard, Patrick and Grotta Ragazzo, Clodoaldo and Santoro Salom\~ao, Pedro A.},
title = {Homoclinic orbits near saddle-center fixed points of {Hamiltonian} systems with two degrees of freedom},
booktitle = {Geometric methods in dynamics (I) : Volume in honor of Jacob Palis},
editor = {de Melo, Wellington and Viana, Marcelo and Yoccoz, Jean-Christophe},
series = {Ast\'erisque},
pages = {151--165},
year = {2003},
publisher = {Soci\'et\'e math\'ematique de France},
number = {286},
mrnumber = {2052300},
zbl = {1044.37044},
language = {en},
url = {https://www.numdam.org/item/AST_2003__286__151_0/}
}
TY - CHAP AU - Bernard, Patrick AU - Grotta Ragazzo, Clodoaldo AU - Santoro Salomão, Pedro A. TI - Homoclinic orbits near saddle-center fixed points of Hamiltonian systems with two degrees of freedom BT - Geometric methods in dynamics (I) : Volume in honor of Jacob Palis AU - Collectif ED - de Melo, Wellington ED - Viana, Marcelo ED - Yoccoz, Jean-Christophe T3 - Astérisque PY - 2003 SP - 151 EP - 165 IS - 286 PB - Société mathématique de France UR - https://www.numdam.org/item/AST_2003__286__151_0/ LA - en ID - AST_2003__286__151_0 ER -
%0 Book Section %A Bernard, Patrick %A Grotta Ragazzo, Clodoaldo %A Santoro Salomão, Pedro A. %T Homoclinic orbits near saddle-center fixed points of Hamiltonian systems with two degrees of freedom %B Geometric methods in dynamics (I) : Volume in honor of Jacob Palis %A Collectif %E de Melo, Wellington %E Viana, Marcelo %E Yoccoz, Jean-Christophe %S Astérisque %D 2003 %P 151-165 %N 286 %I Société mathématique de France %U https://www.numdam.org/item/AST_2003__286__151_0/ %G en %F AST_2003__286__151_0
Bernard, Patrick; Grotta Ragazzo, Clodoaldo; Santoro Salomão, Pedro A. Homoclinic orbits near saddle-center fixed points of Hamiltonian systems with two degrees of freedom, dans Geometric methods in dynamics (I) : Volume in honor of Jacob Palis, Astérisque, no. 286 (2003), pp. 151-165. https://www.numdam.org/item/AST_2003__286__151_0/
[1] , (1964) Instability of dynamical systems with several degrees of freedom, Dokl. Akad. Nauk. 156, pp 9-12. | MR | Zbl
[2] , Homoclinic orbit to a center manifold, to appear in Calc. Var. & P. D. E. | MR | Zbl
[3] , (1999) Shooting methods and topological transversality Proc. R. Soc. Edimb., sec A, Math. 125 No6, pp 1137-1155 | MR | Zbl | DOI
[4] , (1968) Twist mappings, linking, analyticity, and periodic solutions which pass close to an unstable periodic solution, Topological dynamics (Sympos., Colorado State Univ., Ft. Collins, Colo., 1967), pp. 129-153. Benjamin, New York. | MR | Zbl
[5] , (1969), On the ultimate behavior of orbits with respect to an unstable critical point I. Oscillating, asymptotic and capture orbits, Journ. Diff. Eqns 5, pp 136-158. | MR | Zbl | DOI
[6] , , (1979) Homoclinic phenomena for orbits doubly asymptotic to an invariant three-sphere, Indiana Univ. Math. J. 28, pp 211-240. | MR | Zbl | DOI
[7] , (1997) Irregular Dynamics and Homoclinic Orbits to Hamiltonian Saddle Centers, Comm. Pure App. Math. L, pp 105-147. | MR | Zbl
[8] , (1997) On the Stability of Double Homoclinic Loops, Comm. Math. Phys. 184, pp 251-272. | MR | Zbl | DOI
[9] , (1991) Hamiltonian systems with loops of a separatrix of saddle center, Selecta Math. Sov. 10, 1991, pp 297-306. | MR | Zbl
[10] , , (1995) Periodic and homoclinic orbits in two-parameter unfolding of a Hamiltonian system with a homoclinic orbit to a saddle-center, Intern. Jour. Biff. Chaos 5, pp. 397-408. | MR | Zbl | DOI
[11] , , , (1985) Transversality of the invariant manifolds associated to the Lyapunov family of periodic orbits near in the restricted three body problem, Jour. Diff. Eq. 58, pp. 104-156. | MR | Zbl | DOI
[12] , (2000) Oscillatory integrals and phenomena beyond all algebraic orders, Lec. Notes in Maths 1741, Springer. | MR | Zbl
[13] , (1990) Topological methods for discrete dynamical systems, GAMM-Mitteilungen, Heft-2, pp. 19-37. | MR | Zbl
[14] , , and , (1992) Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle center, J. Dyn. Diff. Eqns. 4, pp. 95-126. | MR | Zbl | DOI
[15] , (1958) On the generalization of a theorem of A. Liapunoff, Comm. Pure Appl. Math. v. 11, pp. 257-271. | MR | Zbl | DOI
[16] , (1973) Stable and random motions in dynamical systems, Ann. Math. Stud. 77, Princeton University Press. | MR | Zbl
[17] , (1964) Über das Verhalten analytischer Hamiltonscher Differentialgle-ichungen in der Nähe einer Gleichgewichtslösung, Math. Ann. v. 154, pp. 285-300. Princeton University Press. | MR | Zbl | EuDML | DOI
[18] , , (2000) Central stable/unstable manifolds and the destruction of tori in the restricted planar Hill problem, Physica D 140, pp 1-32. | MR | Zbl | DOI







