Download Chaos and Statistical Methods: Proceedings of the Sixth by K. Tomita (auth.), Professor Dr. Yoshiki Kuramoto (eds.) PDF

By K. Tomita (auth.), Professor Dr. Yoshiki Kuramoto (eds.)

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Additional resources for Chaos and Statistical Methods: Proceedings of the Sixth Kyoto Summer Institute, Kyoto, Japan September 12–15, 1983

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4) respectively. YOSHIDA 5) showed that the appearance of at least one irrational or imaginary Kowalevski's exponent means the non-existence of another algebraic ( and analytic) first integral independent of Hami Itonian. In the range -48<£<0. the exponents in both cases become imaginary (complex conjugate pair), and therefore the Hami Itonian system (1) is non-integrable. In this case it can be proved that H (Hamiltonian) is proportional to the arbitrary constant 16. and since H=O for our initial condition.

Va. Rachko: "Singularities of the Transition to a Turbulent t

When 0 > OF all eigenvalues approach 1 with liN corrections. Table 2. Convergence of OF when p = 1/4. 1) and N is the largest size lattice used in the fit. t the spectrum may actually be continuous between 0 and 1 with an isolated ~o > 1 w~en < 0*. The Pade analysis could easily miss this fact. It is interesting to note that liN decays have been observed in other dynamical systems which are hyperbolic except at isolated points [12]. P. Kadanoff for many stimulating discussions. This work was supported in part by NSF Grant #80-20609 at the University of Chicago.

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