Publication Cover
Applicable Analysis
An International Journal
Volume 31, 1988 - Issue 3
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Original Articles

Bifurcation of periodic orbits for non-positive definite hamiltonian systems

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Pages 163-199 | Received 20 Jul 1988, Published online: 02 May 2007

References

  • Abraham , R. and Marsden , J.E. 1978 . Foundations of mechanics , Massachusetts : Benjamin/Oummings .
  • Arnol'd , V.I. 1971 . On matrices depending on parameters . Russian Math. Surveys , 26 : 29 – 43 .
  • Birkhoff , G.D. 1927 . Dynamical systems , New York : A.M.S. Coll, IX .
  • Borgoyne , N. and Cushman , R. 1974 . Normal forms for real linear Hamiltonian systems with purely imaginary eigenvalues . Cel, Mech , 8 : 435 – 443 .
  • Chow , S.N. and Mallet-Paret , J. . Periodic solutions near an equilibrium of a non-positive definite Hamiltonian system . Unpublished preprint
  • Cushman , R. , Deprit , A. and Mosak , R. 1983 . Normal form and representation theory . J. Math. Phys , 24 : 2103 – 2116 .
  • Cushman , R. . Notes on Normal form . Michigan State University .
  • Deprit , A. , Henrad , J. , Price , J.f. and Rom , A. 1969 . Birkhoffs normalization . Cel, Mech , 1 : 225 – 251 .
  • Fadel , E. and Rabinowitz . 1977 . Bifurcation for Odd potential operators and an Alternative Topological Index . J. of Functional Analysis , 26 : 48 – 67 .
  • Galin , D.M. . Versal deformations of linear Hamiltonian systems . Michigan State University .
  • Hale , J.K. 1980 . Ordinary Differential Equations , New York : Kreiger Publ. Co .
  • Humphreys , J.E. 1972 . Introduction to Lie algebras and representation theory , New York : Springer-Verlag .
  • Kocak , H. 1984 . Normal forms and versal deformations of linear Hamiltonian systems . J, Diff , 51 : 359 – 107 .
  • van der Meer , J.C. 1982 . Nonsemisimple 1: 1 resonance at an equilibrium . Cel. mech , 27 : 131 – 149 .
  • van der Meer , J.C. 1985 . The Hamiltonian Hopf bifurcations , University of Utrecht : Doctoral thesis .
  • Moser , J. 1968 . Lectures on Hamiltonian systems . Mem. A.M.S , 81 : 1 – 60 .
  • Moser , J. 1976 . Periodic orbits near an equilibrium and a theorem by Alan Weinstein . Comm. Pure Appl. Math , 29 : 272 – 747 .
  • Siegel , C.L. and Moser , J.K. 1971 . Lectures on celestial mechanics , Verlag : Springer .
  • Weinstein , A. 1973 . Normal modes for non-linear Hamiltonian systems . Inv. Math , 2 : 47 – 57 .

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