Open AccessPERIOD BIFURCATIONS OF THE STANDARD MAPPING AND THE TRANSITIONS FROM THEM TO CHAOS
Author(s) -
Junxian Liu,
Guangzhi Chen,
Guangrui Wang,
Shigang Chen
Publication year - 1988
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.37.119
Subject(s) - period doubling bifurcation , scaling , bifurcation , period (music) , chaotic , physics , sequence (biology) , chaos (operating system) , standard map , periodic orbits , statistical physics , mathematical analysis , mathematics , geometry , classical mechanics , nonlinear system , quantum mechanics , computer science , computer security , artificial intelligence , biology , acoustics , genetics
The behavior of periodic orbits of the standard mapping near their residues R =1 and R = 0 is studied. There is a sequence of period doubling bifurcations corresponding to the former, the bifurcation ratio δ and scaling factors α and βagree with those obtained from other two-dimensional area-preserving mappings. There are same period bifurcations corresponding to the latter, which is related to the antisymetric nature of the standard mapping. Moreover, by calculating Lyaponov exponents of chaotic orbits, we have found near the accumulation point k∞ of a sequence of period doubling bifurcations a scaling relation λ=λ∞+A(k-k∞)+B(k-k∞)τ with τ≈0.32, it agrees with the result τ=ln(2)/ln(δ)(δ=8.7210972…) conjectured theoretically.