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.
|Original language||English (US)|
|Number of pages||6|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|State||Published - Jun 12 2000|
ASJC Scopus subject areas
- Physics and Astronomy(all)