02515nam a22003735i 4500978-3-642-57884-7cr nn 008mamaa110811s1994 gw : s :::: 0:eng d9783642578847ENGDEQA299.6-433515Online resource: SpringerDynamical Systems V[EBook]Bifurcation Theory and Catastrophe Theoryedited by V. I. Arnolâ€™d.Berlin, HeidelbergSpringer1994.IX, 274 pagesonline resource.textonline resourceEncyclopaedia of Mathematical Sciences,0938-0396 ;5Bifurcation theory and catastrophe theory are two of the best known areas within the field of dynamical systems. Both are studies of smooth systems, focusing on properties that seem to be manifestly non-smooth. Bifurcation theory is concerned with the sudden changes that occur in a system when one or more parameters are varied. Examples of such are familiar to students of differential equations, from phase portraits. Moreover, understanding the bifurcations of the differential equations that describe real physical systems provides important information about the behavior of the systems. Catastrophe theory became quite famous during the 1970's, mostly because of the sensation caused by the usually less than rigorous applications of its principal ideas to "hot topics", such as the characterization of personalities and the difference between a "genius" and a "maniac". Catastrophe theory is accurately described as singularity theory and its (genuine) applications. The authors of this book, the first printing of which was published as Volume 5 of the Encyclopaedia of Mathematical Sciences, have given a masterly exposition of these two theories, with penetrating insight.Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)Mathematics.Mathematical analysis.Analysis (Mathematics).Statistical physics.Dynamical systems.Mathematics.Analysis.Statistical Physics, Dynamical Systems and Complexity.Arnold, Vladimir Igorevic1937-2010.editor.SpringerLink (Online service)Encyclopaedia of Mathematical Sciences,5http://dx.doi.org/10.1007/978-3-642-57884-7