A New Interpretation of the Symbolic Codes for the Hénon Map. II | Zendy

Yoshihiro Yamaguchi | Zendy; Kiyotaka Tanikawa | Zendy

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A New Interpretation of the Symbolic Codes for the Hénon Map. II

Author(s) -

Yoshihiro Yamaguchi,

Kiyotaka Tanikawa

Publication year - 2011

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.125.435

Subject(s) - symbol (formal) , orbit (dynamics) , physics , block (permutation group theory) , resonance (particle physics) , word (group theory) , plane (geometry) , braid , sequence (biology) , chain (unit) , interpretation (philosophy) , combinatorics , mathematics , geometry , quantum mechanics , computer science , materials science , biology , engineering , composite material , genetics , programming language , aerospace engineering

After the completion of the horseshoe for the Henon map, periodic orbits and homoclinic orbits are characterized by the symbolic code represented by 0's and 1's. Seven problems for these codes are proposed. The resonance regions are constructed using the stable and unstable manifolds of saddle points appearing through the rotational bifurcation of the el- liptic fixed point. On the basis of the concept of resonance regions, the code is separated into several blocks. Separated blocks are represented by new four block words. Thus, all periodic orbits and homoclinic orbits are represented by these codes. On the basis of the concept of block structure, we obtain the complete or partial answers or the conjecture to these problems. Subject Index: 030

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