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Volumn 6, Issue 6, 1996, Pages 991-1006

Families of transverse poincaré homoclinic orbits in 2n-dimensional Hamiltonian systems close to the system with a loop to a saddle-center

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EID: 0039015625     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127496000540     Document Type: Article
Times cited : (24)

References (27)
  • 3
    • 0001799504 scopus 로고
    • Symplectic geometry and its applications
    • eds. Arnol'd, V. I & Novikov, S. P. (Springer Verlag, New York)
    • Arnold, V. I. & Givental, A. B. [1990] "Symplectic geometry and its applications," in Dynamical Systems IV, eds. Arnol'd, V. I & Novikov, S. P. (Springer Verlag, New York).
    • (1990) Dynamical Systems , vol.4
    • Arnold, V.I.1    Givental, A.B.2
  • 4
    • 0039948263 scopus 로고
    • Non-integrability of the problem of motion around an oblate planet
    • Celletti, A. & Negrini., P. [1995] "Non-integrability of the problem of motion around an oblate planet," Cel. Mech. Dynam. Astron. 61, 253-260.
    • (1995) Cel. Mech. Dynam. Astron. , vol.61 , pp. 253-260
    • Celletti, A.1
  • 5
    • 84968172188 scopus 로고
    • Examples of nonintegrable analytic Hamiltonian vector fields with no small divisors
    • Cushman, R. [1978] "Examples of nonintegrable analytic Hamiltonian vector fields with no small divisors," Trans. Amer. Math. Soc. 238(1), 45-55.
    • (1978) Trans. Amer. Math. Soc. , vol.238 , Issue.1 , pp. 45-55
    • Cushman, R.1
  • 6
    • 0001306130 scopus 로고
    • Transversal homoclinic orbits in an integrable system
    • Devaney, R. L. [1978] "Transversal homoclinic orbits in an integrable system", Am. J. of Math. 100(3), 631-642.
    • (1978) Am. J. of Math. , vol.100 , Issue.3 , pp. 631-642
    • Devaney, R.L.1
  • 8
    • 0002499757 scopus 로고
    • Versal deformations of linear hamiltonian systems
    • MGU Publ. House, in Russian
    • Galin, D. M. [1975] "Versal deformations of linear Hamiltonian systems," in Trudy Petrovsky's Seminar 1 (MGU Publ. House), pp. 63-74 (in Russian).
    • (1975) Trudy Petrovsky's Seminar , vol.1 , pp. 63-74
    • Galin, D.M.1
  • 9
    • 21144468600 scopus 로고
    • Center-stable manifold theorem for differential equations in banach spaces
    • Gallay, Th. [1993] "Center-stable manifold theorem for differential equations in banach spaces," Comm. Math. Phys. 138, 249-268.
    • (1993) Comm. Math. Phys. , vol.138 , pp. 249-268
    • Gallay, Th.1
  • 10
    • 21844502216 scopus 로고
    • Nonintegrability of some Hamiltonian systems, scattering and analytic continuation
    • Grotta Ragazzo, C. [1994] "Nonintegrability of some Hamiltonian systems, scattering and analytic continuation," Comm. Math. Phys. 166, 155-177.
    • (1994) Comm. Math. Phys. , vol.166 , pp. 155-177
    • Grotta Ragazzo, C.1
  • 11
    • 34249767926 scopus 로고
    • On the motion of two-dimensional vortices with mass
    • Grotta Ragazzo, C., Koiller, J. & Oliva, W. M. [1994] "On the motion of two-dimensional vortices with mass," J. Nonlin. Sci. 4(5), 375-418.
    • (1994) J. Nonlin. Sci. , vol.4 , Issue.5 , pp. 375-418
    • Grotta Ragazzo, C.1    Koiller, J.2    Oliva, W.M.3
  • 13
    • 21844492041 scopus 로고
    • Periodic and homoclinic orbits in a two-parameter unfolding of a Hamiltonian system with a homoclinic orbit to a saddle-center
    • Koltsova, O. Yu. & Lerman, L. M. [1995] "Periodic and homoclinic orbits in a two-parameter unfolding of a Hamiltonian system with a homoclinic orbit to a saddle-center," Int. J. Bifurcation and Chaos 5(2), 397-408.
    • (1995) Int. J. Bifurcation and Chaos , vol.5 , Issue.2 , pp. 397-408
    • Koltsova, O.Yu.1    Lerman, L.M.2
  • 15
    • 0039948260 scopus 로고
    • Hamiltonian systems with a separatrix loop of a saddle-center
    • ed. Leontovich-Andronova, E. A. (Gorky State Univ.), in Russian
    • Lerman, L. M. [1987] "Hamiltonian systems with a separatrix loop of a saddle-center," in Methods of Qualitative Theory of Diff. Eq., ed. Leontovich-Andronova, E. A. (Gorky State Univ.), pp. 89-103 (in Russian) [Engl. transl. in Selecta Math. Sov. 10, 297, (1991)].
    • (1987) Methods of Qualitative Theory of Diff. Eq. , pp. 89-103
    • Lerman, L.M.1
  • 16
    • 0000084628 scopus 로고
    • Lerman, L. M. [1987] "Hamiltonian systems with a separatrix loop of a saddle-center," in Methods of Qualitative Theory of Diff. Eq., ed. Leontovich-Andronova, E. A. (Gorky State Univ.), pp. 89-103 (in Russian) [Engl. transl. in Selecta Math. Sov. 10, 297, (1991)].
    • (1991) Selecta Math. Sov. , vol.10 , pp. 297
  • 17
    • 0000199807 scopus 로고
    • 2 within extended neighborhoods of simple singular points. II
    • in Russian
    • 2 within extended neighborhoods of simple singular points. II," Matemat. Sbornik 184(4), 105-138, (in Russian) [Engl. transl. in Russian Acad. Sci. Sb. Math. 78(2), 479-506 (1994)].
    • (1993) Matemat. Sbornik , vol.184 , Issue.4 , pp. 105-138
    • Lerman, L.M.1    Umanskii, Ya.L.2
  • 18
    • 0040251159 scopus 로고
    • 2 within extended neighborhoods of simple singular points. II," Matemat. Sbornik 184(4), 105-138, (in Russian) [Engl. transl. in Russian Acad. Sci. Sb. Math. 78(2), 479-506 (1994)].
    • (1994) Russian Acad. Sci. Sb. Math. , vol.78 , Issue.2 , pp. 479-506
  • 20
    • 0003540692 scopus 로고
    • Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems
    • Springer-Verlag, New York
    • Mielke, A. [1993] "Hamiltonian and Lagrangian flows on center manifolds with applications to elliptic variational problems," Lecture Notes in Mathematics 1489 (Springer-Verlag, New York).
    • (1993) Lecture Notes in Mathematics , vol.1489
    • Mielke, A.1
  • 21
    • 0002635502 scopus 로고
    • Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center
    • Mielke, A., Holmes, P. & O'Reilly, O. [1992] "Cascades of homoclinic orbits to, and chaos near, a Hamiltonian saddle-center," J. Dyn. Diff. Eq. 4, 95-126.
    • (1992) J. Dyn. Diff. Eq. , vol.4 , pp. 95-126
    • Mielke, A.1    Holmes, P.2    O'Reilly, O.3
  • 22
    • 0004190360 scopus 로고
    • Princeton, University Press, Princeton, New Jersey
    • Milnor, J. [1963] Morse Theory (Princeton, University Press, Princeton, New Jersey).
    • (1963) Morse Theory
    • Milnor, J.1
  • 23
    • 49849128478 scopus 로고
    • On morse smale dynamical systems
    • Palis, J. [1969] "On Morse Smale dynamical systems," Topology 8, 385-405.
    • (1969) Topology , vol.8 , pp. 385-405
    • Palis, J.1
  • 24
    • 0002995706 scopus 로고
    • Structure of an expanded neighborhood of a coarse saddle-focus equilibrium state
    • Shil'nikov, L. P. [1970] "Structure of an expanded neighborhood of a coarse saddle-focus equilibrium state" (in Russian), Math. Sb. (Nov. Seriya) 81, 92.
    • (1970) Math. Sb. (Nov. Seriya) , vol.81 , pp. 92
    • Shil'nikov, L.P.1
  • 25
    • 22244441450 scopus 로고
    • Topology and mechanics. I
    • Smale, S. [1970] "Topology and mechanics. I," Invent. Math. 10(4), 305-331.
    • (1970) Invent. Math. , vol.10 , Issue.4 , pp. 305-331
    • Smale, S.1
  • 26
    • 0001316020 scopus 로고
    • On the algebraic problem concerning the normal forms of linear dynamical system
    • Williamson, J. [1936] "On the algebraic problem concerning the normal forms of linear dynamical system," Amer. J. Math. 58(1), 141-163.
    • (1936) Amer. J. Math. , vol.58 , Issue.1 , pp. 141-163
    • Williamson, J.1
  • 27
    • 0001118559 scopus 로고
    • On Hamiltonian systems with homoclinic saddle curves
    • Turaev, D. V. & Shil'nikov, L. P. [1989] "On Hamiltonian systems with homoclinic saddle curves," Soviet Math. Dokl. 39, 165-168.
    • (1989) Soviet Math. Dokl. , vol.39 , pp. 165-168
    • Turaev, D.V.1    Shil'nikov, L.P.2


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