UNSTABLE DIMENSION VARIABILITY AND COMPLEXITY IN CHAOTIC SYSTEMS

We examine the interplay between complexity and unstable periodic orbits in high-dimensional chaotic systems. Argument and numerical evidence are presented suggesting that complexity can arise when the system is severely nonhyperbolic in the sense that periodic orbits with a distinct number of unstable directions coexist and are densely mixed. A quantitative measure is introduced to characterize this unstable dimension variability. @S1063-651X~99!51404-9#

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