TY - JOUR
T1 - Characterization of transition to chaos with multiple positive Lyapunov exponents by unstable periodic orbits
AU - Davidchack, Ruslan
AU - Lai, Ying-Cheng
PY - 2000/6/12
Y1 - 2000/6/12
N2 - We investigate how the transition to chaos with multiple positive Lyapunov exponents can be characterized by the set of infinite number of unstable periodic orbits embedded in the chaotic invariant set. We argue and provide numerical confirmation that the transition is generally accompanied by a nonhyperbolic behavior: unstable dimension variability. As a consequence, the Lyapunov exponents, except for the largest one, pass through zero continuously. (C) 2000 Elsevier Science B.V.
AB - We investigate how the transition to chaos with multiple positive Lyapunov exponents can be characterized by the set of infinite number of unstable periodic orbits embedded in the chaotic invariant set. We argue and provide numerical confirmation that the transition is generally accompanied by a nonhyperbolic behavior: unstable dimension variability. As a consequence, the Lyapunov exponents, except for the largest one, pass through zero continuously. (C) 2000 Elsevier Science B.V.
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U2 - 10.1016/S0375-9601(00)00335-2
DO - 10.1016/S0375-9601(00)00335-2
M3 - Article
AN - SCOPUS:0034640660
SN - 0375-9601
VL - 270
SP - 308
EP - 313
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 6
ER -