On the Bifurcation of the Periodic Orbits in Certain Hamiltonian Systems
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概要
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The nature of the bifurcation of the fixed points which become stable or unstablealternately on changing a parameter p is studied phenomenolccgically by a two-dimensional area-preserving mapping. It is shown that 1.he fixed point generally changes itscharacter sequentially as elliptic, ordinary hyperbolic, elliptic, reflection hyperbolic,elliptic, ordinary hyperbolic, and so on, and the values of the parameter p. when thestable fixed (elliptic) point changes to unstable fixed point (hyperbolic of either type)define a ratio J = ( p. - p. .) / ( p... - p.) which ternds for k= cC to either one of l, cX),or exp (z / ex) where a is a constant depending on the system, as far as in examples examined here. Two hamiltonian systems which prc>vide (>=CXP (n/J -2 ) and 1 are dis-cussed in the light of the present formalism.[bifurcation of fixed point, area-preserving mapping, Feigettbaum ratio, periodic l1 orbit1
- 社団法人日本物理学会の論文
- 1989-02-15
著者
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Shimizu Yasushi
Department Of Obstetrics And Gynecology Akita University Graduate School Of Medicine
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Saito Nobuhiko
Department Of Applied Physics School Of Science And Engineering Waseda University
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Takeda Takeshi
Department Of Applied Biology Faculty Of Textile Science Kyoto Institute Of Technology
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Takeda Takeshi
Department Of Applied Physics Waseda University
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Shimizu Yasushi
Department Of Anatomy Tokyo Dental College
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Shimizu Yasushi
Department Of Applied Physics Waseda University
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Saito Nobuhiko
Department Of Applied Physics And Science And Engineering Research Institute Waseda University
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