Non-Birkhoff Orbits with 2n Turning Points in the Standard Map | Zendy

Kiyotaka Tanikawa | Zendy; Yoshiyuki Y. Yamaguchi | Zendy

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Non-Birkhoff Orbits with 2n Turning Points in the Standard Map

Author(s) -

Kiyotaka Tanikawa,

Yoshiyuki Y. Yamaguchi

Publication year - 2003

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.109.187

Subject(s) - bifurcation , saddle point , physics , periodic orbits , period doubling bifurcation , fixed point , saddle , standard map , period (music) , mathematical analysis , mathematical physics , mathematics , classical mechanics , geometry , nonlinear system , chaotic , quantum mechanics , computer science , mathematical optimization , acoustics , artificial intelligence

One of the two fixed points of the standard map gives rise to a period-doubling bifurcation and becomes a saddle with reflection beyond a certain parameter value. In association with this bifurcation, symmetric non-Birkhoff periodic orbits (SNBOs) with 2n (n ≥ 2) turning points appear and exhibit complicated behavior. We first analyze the structure of stable and unstable manifolds of this saddle and then derive dynamical order relations for these SNBOs and show that a period-3 SNBO implies the existence of SNBOs with all possible numbers of turning points.

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