Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1998-04-13
Nonlinear Sciences
Chaotic Dynamics
11 pages (LaTex), 3 Postscript figures
Scientific paper
The asymptotic distance between trajectories $d_{\infty}$, is studied in detail to characterize the occurrence of chaos. We show that this quantity is quite distinct and complementary to the Lyapunov exponents, and it allows for a quantitave estimate for the folding mechanism which keeps the motion bounded in phase space. We study the behaviour of $d_{\infty}$ in simple unidimensional maps. Near a critical point $d_{\infty}$ has a power law dependence on the control parameter. Furthermore, at variance with the Lyapunov exponents, it shows jumps when there are sudden changes on the available phase-space.
Baran Virgil
Bonasera Aldo
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