We determined the exact location of the shearless KAM curve in the quadratic map and numerically investigate the breakup thresholds of those curves in the entire parameter space. The breakup diagram reveals many sharp singularities like fractals on the reconnection thresholds of the twin-chains with rational rotation numbers.Comment: 5 latex pages, 5 postscript figures, to be published in Prog.Theor.Phy

Reconnection processes of twin-chains are systematically studied in the quadratic twist map. By using the reversibility and symmetry of the mapping, the location of the indicator points is theoretically determined in the phase space. The indicator points enable us to obtain useful information about the reconnect ion processes and the transition to global chaos. We succeed in deriving the general conditions for the reconnection thresholds. In addition, a new type of reconnect ion process which generates shearless curves is studied.(1·1) (1·2)

The computer experiments are carried out on the phenomena of self-synchronization in a many-mode system described by the van der Pol type equation. The results are successfully explained in terms of the perturbation theory based on a mean field approximation proposed in a previous article. The extension of the theory to further complicated phenomena of mode-locking is briefly cliscussed.

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Self-organized collective behavior in globally coupled multimode lasers is investigated by introducing a new physical quantity, gain circulation, that characterizes the gain transfer among lasing modes. Numerical simulations indicate that the self-organization is established such that the gain circulations in all the closed interaction paths involving arbitrary multiple lasing modes become negligibly small as compared with direct mode-to-mode gain circulations. This implies that the nonreciprocal local (i.e., modeto-mode) gain transfers are self-organized so as to ensure reciprocal average gain flow among modes approximately and that temporal evolutions of individual mode intensities are determined accordingly.