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Heteroclinic orbits for a class of Hamiltonian systems on Riemannian manifolds
1. | Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China, China |
2. | Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona |
References:
[1] |
V. I. Arnold, "Mathematial Methods of Classical Mechanics," 2nd edition, Springer, New York, 1989. |
[2] |
A. V. Bolsinov and A. T. Fomenko, "Integrable Hamiltonian Systems: Geometry, Topology and Classification," Chapman & Hall/CRC, Boca Raton, FL, 2004. |
[3] |
K. Burns and M. Gidea, "Differential Geometry and Topology: With a View to Dynamical Systems," Studies in Advanced Mathematics, Chapman & Hall/CRC, Boca Raton, FL, 2005. |
[4] |
E. Canalias and J. J. Masdemont, Homoclinic and heteroclinic transfer trajectories between planar Lyapunov orbits in the sun-earth and earth-moon systems, Discrete Contin. Dyn. Syst., 14 (2006), 261-279. |
[5] |
P. C. Carriã and O. H. Miyagaki, Existence of homoclinic solutions for a class of time dependent Hamiltonian systems, J. Math. Anal. Appl., 230 (1999), 157-172.
doi: 10.1006/jmaa.1998.6184. |
[6] |
Ch. N. Chen and S. Y. Tzeng, Periodic solutions and their connecting orbits of Hamiltonian systems, J. Diff. Eqns., 177 (2001), 121-145.
doi: 10.1006/jdeq.2000.3996. |
[7] |
C. Chen, F. Liu and X. Zhang, Orthogonal separable Hamitonian systems on $T^2$, Science in China Ser. A, 50 (2007), 1725-1737.
doi: 10.1007/s11425-007-0156-7. |
[8] |
M. do Carmo, "Riemannian Geometry," Birkhaser, Boston, 1992. |
[9] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," 2nd edition, Springer, Berlin, 1983. |
[10] |
M. Izydorek and J. Janczewska, Homoclinic solutions for a class of the second order Hamiltonian systems, J. Diff. Eqns., 219 (2005), 375-389.
doi: 10.1016/j.jde.2005.06.029. |
[11] |
M. Izydorek and J. Janczewska, Heteroclinic solutions for a class of the second order Hamiltonian systems, J. Diff. Eqns., 238 (2007), 381-393.
doi: 10.1016/j.jde.2007.03.013. |
[12] |
J. Milnor, "Morse Theory," Princenton University Press, Princenton, 1963. |
[13] |
J. Moser, "Selected Chapters in the Calculus of Variations," Birkhäuser, Basel, 2003. |
[14] |
P. H. Rabinowitz, Periodic and heteroclinic orbits for a periodic Hamiltonian system, Ann. Inst. H. Poincaré, 6 (1989), 311-346. |
[15] |
P. H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), 33-38. |
[16] |
P. H. Rabinowitz, Connecting orbits for a reversible Hamiltonian systems, Ergodic Theory Dynam. Systems, 20 (2000), 1767-1784.
doi: 10.1017/S0143385700000985. |
[17] |
P. H. Rabinowitz, Variational methods for Hamiltonian systems, in "Handbood of Dynamical Sysstems," Vol. 1A, Elsevier, Amsterdam, (2002), 1091-1127. |
[18] |
P. H. Rabinowitz and K. Tanaka, Some results on connecting orbits for a class of Hamiltonian systems, Math. Z., 206 (1991), 472-499.
doi: 10.1007/BF02571356. |
[19] |
W. Rudin, "Real and Complex Analysis," 3rd edition, McGraw-Hill Book Co., New York, 1987. |
[20] |
A. Szulkin and W. Zou, Homoclinic orbits for asymptotically linear Hamiltonian systems, J. Funct. Anal., 187 (2001), 25-41.
doi: 10.1006/jfan.2001.3798. |
show all references
References:
[1] |
V. I. Arnold, "Mathematial Methods of Classical Mechanics," 2nd edition, Springer, New York, 1989. |
[2] |
A. V. Bolsinov and A. T. Fomenko, "Integrable Hamiltonian Systems: Geometry, Topology and Classification," Chapman & Hall/CRC, Boca Raton, FL, 2004. |
[3] |
K. Burns and M. Gidea, "Differential Geometry and Topology: With a View to Dynamical Systems," Studies in Advanced Mathematics, Chapman & Hall/CRC, Boca Raton, FL, 2005. |
[4] |
E. Canalias and J. J. Masdemont, Homoclinic and heteroclinic transfer trajectories between planar Lyapunov orbits in the sun-earth and earth-moon systems, Discrete Contin. Dyn. Syst., 14 (2006), 261-279. |
[5] |
P. C. Carriã and O. H. Miyagaki, Existence of homoclinic solutions for a class of time dependent Hamiltonian systems, J. Math. Anal. Appl., 230 (1999), 157-172.
doi: 10.1006/jmaa.1998.6184. |
[6] |
Ch. N. Chen and S. Y. Tzeng, Periodic solutions and their connecting orbits of Hamiltonian systems, J. Diff. Eqns., 177 (2001), 121-145.
doi: 10.1006/jdeq.2000.3996. |
[7] |
C. Chen, F. Liu and X. Zhang, Orthogonal separable Hamitonian systems on $T^2$, Science in China Ser. A, 50 (2007), 1725-1737.
doi: 10.1007/s11425-007-0156-7. |
[8] |
M. do Carmo, "Riemannian Geometry," Birkhaser, Boston, 1992. |
[9] |
D. Gilbarg and N. S. Trudinger, "Elliptic Partial Differential Equations of Second Order," 2nd edition, Springer, Berlin, 1983. |
[10] |
M. Izydorek and J. Janczewska, Homoclinic solutions for a class of the second order Hamiltonian systems, J. Diff. Eqns., 219 (2005), 375-389.
doi: 10.1016/j.jde.2005.06.029. |
[11] |
M. Izydorek and J. Janczewska, Heteroclinic solutions for a class of the second order Hamiltonian systems, J. Diff. Eqns., 238 (2007), 381-393.
doi: 10.1016/j.jde.2007.03.013. |
[12] |
J. Milnor, "Morse Theory," Princenton University Press, Princenton, 1963. |
[13] |
J. Moser, "Selected Chapters in the Calculus of Variations," Birkhäuser, Basel, 2003. |
[14] |
P. H. Rabinowitz, Periodic and heteroclinic orbits for a periodic Hamiltonian system, Ann. Inst. H. Poincaré, 6 (1989), 311-346. |
[15] |
P. H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proc. Roy. Soc. Edinburgh Sect. A, 114 (1990), 33-38. |
[16] |
P. H. Rabinowitz, Connecting orbits for a reversible Hamiltonian systems, Ergodic Theory Dynam. Systems, 20 (2000), 1767-1784.
doi: 10.1017/S0143385700000985. |
[17] |
P. H. Rabinowitz, Variational methods for Hamiltonian systems, in "Handbood of Dynamical Sysstems," Vol. 1A, Elsevier, Amsterdam, (2002), 1091-1127. |
[18] |
P. H. Rabinowitz and K. Tanaka, Some results on connecting orbits for a class of Hamiltonian systems, Math. Z., 206 (1991), 472-499.
doi: 10.1007/BF02571356. |
[19] |
W. Rudin, "Real and Complex Analysis," 3rd edition, McGraw-Hill Book Co., New York, 1987. |
[20] |
A. Szulkin and W. Zou, Homoclinic orbits for asymptotically linear Hamiltonian systems, J. Funct. Anal., 187 (2001), 25-41.
doi: 10.1006/jfan.2001.3798. |
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