论文信息 - Transition Phenomena in Nonlinear Systems

Transition Phenomena in Nonlinear Systems

Since this workshop brings together mathematicians, on the one hand, and research workers in the field of natural sciences, on the other, I will try to present the basic ideas of my talk in a form which is not too technical. Furthermore I can omit details because they are laid down in a number of recent articles and a book of mine [1],[2]. I shall first outline what I mean by transition phenomena. As will transpire from the examples, the general feature common to the transition phenomena I treat here are dramatic changes on macroscopic scales.

H. Haken | H. Haken

[1] Hermann Haken,et al. Dynamics of Synergetic Systems , 1980 .

[2] W. Gähler. R. Abraham and J. Robbin, Transversal Mappings and Flows. X + 161 S. m. Fig. New York/Amsterdam 1967. W. A. Benjamin, Inc. Preis geb. $ 12,50 , 1969 .

[3] Hermann Haken,et al. Laserlight — first example of a second-order phase transition far away from thermal equilibrium , 1970 .

[4] Grégoire Nicolis,et al. Self-Organization in nonequilibrium systems , 1977 .

[5] K. Kaplan. H. Haken, Synergetics. An Introduction. Nonequilibrium Phase Transitions and Self-Organization in Physics, Chemistry, and Biology (2nd Edition). XI + 355 S., 152 Abb. Berlin—Heidelberg—New York 1978. Springer-Verlag. DM 66,00 , 1980 .

[6] J. Yorke,et al. Period Three Implies Chaos , 1975 .

[7] G. Ahlers,et al. Turbulence near Onset of Convection , 1980 .

[8] A. Kelley. The stable, center-stable, center, center-unstable, unstable manifolds , 1967 .

[9] Sir Alan Cottrell F.R.S.. Structural stability in physics , 1980 .

[10] R. G. Lerner,et al. Encyclopedia of Physics , 1990 .

[11] H. Haken. Pattern Formation by Dynamic Systems and Pattern Recognition , 1979, Springer Series in Synergetics.