Coding Rules for Symmetric Periodic OrbitsAppearing through the Period-doubling Bifurcation

YAMAGUCHI Yoshihiro, TANIKAWA Kiyotaka

doi:10.50916/rnaoj.21.0_1

Bibliographic Information

Other Title

周期倍分岐で生じた対称周期軌道の記号則

Abstract

Consider the two-dimensional area-preserving map which satisfies the condition that the Smale horseshoe exists at a ≥ a_c > 0. In the horseshoe, every periodic orbit is uniquely coded by two symbols 0 and 1. As a result, the symbol sequence s represented by 0 and 1 is determined. For the periodic orbit, the symbol sequence s is the repetition of a finite number of symbols named the code. Suppose that the mother periodic orbit M undergoes the period-doubling bifurcation. Then, the first generation of daughter periodic orbit D₁ appears from M. The n (≥ 1)-th generation of daughter periodic orbit D_n is also defined. Let P₀ be the code for M and P_n be the code for D_n (n ≥ 1). Our purpose is to derive the coding rule to determine P_n from the given P₀. The coding rules for the restricted symmetric periodic orbits are derived.

Journal

Report of the National Astronomical Observatory of Japan

Report of the National Astronomical Observatory of Japan 21 (0), 1-20, 2021

Inter-University Research Institute Corporation National Institutes of Natural Sciences, National Astronomical Observatory of Japan

Details 詳細情報について

CRID: 1390288015472321408

NII Article ID: 130008038000

DOI: 10.50916/rnaoj.21.0_1

ISSN: 24361402; 09156321

Text Lang: ja

Data Source

JaLC
CiNii Articles

Abstract License Flag: Allowed

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