Catastrophe theory

About: Catastrophe theory is a research topic. Over the lifetime, 1236 publications have been published within this topic receiving 28013 citations.

Singularities and groups in bifurcation theory

Abstract: This book has been written in a frankly partisian spirit-we believe that singularity theory offers an extremely useful approach to bifurcation prob- lems and we hope to convert the reader to this view In this preface we will discuss what we feel are the strengths of the singularity theory approach This discussion then Ieads naturally into a discussion of the contents of the book and the prerequisites for reading it Let us emphasize that our principal contribution in this area has been to apply pre-existing techniques from singularity theory, especially unfolding theory and classification theory, to bifurcation problems Many ofthe ideas in this part of singularity theory were originally proposed by Rene Thom; the subject was then developed rigorously by John Matherand extended by V I Arnold In applying this material to bifurcation problems, we were greatly encouraged by how weil the mathematical ideas of singularity theory meshed with the questions addressed by bifurcation theory Concerning our title, Singularities and Groups in Bifurcation Theory, it should be mentioned that the present text is the first volume in a two-volume sequence In this volume our emphasis is on singularity theory, with group theory playing a subordinate role In Volume II the emphasis will be more balanced Having made these remarks, Iet us set the context for the discussion of the strengths of the singularity theory approach to bifurcation As we use the term, bifurcation theory is the study of equations with multiple solutions

Charged AdS black holes and catastrophic holography

Abstract: We compute the properties of a class of charged black holes in anti--de Sitter space-time, in diverse dimensions. These black holes are solutions of consistent Einstein-Maxwell truncations of gauged supergravities, which are shown to arise from the inclusion of rotation in the transverse space. We uncover rich thermodynamic phase structures for these systems, which display classic critical phenomena, including structures isomorphic to the van der Waals--Maxwell liquid-gas system. In that case, the phases are controlled by the universal ``cusp'' and ``swallowtail'' shapes familiar from catastrophe theory. All of the thermodynamics is consistent with field theory interpretations via holography, where the dual field theories can sometimes be found on the world volumes of coincident rotating branes.

A rational route to randomness

Abstract: Complex dynamics in economics arise from nonlinear systems that do not converge to a fixed point, a limit cycle, or explode or implode exponentially due to endogenous factors. They arise from cybernetics, catastrophe theory, chaos theory, or the varieties of modern complexity theory, including models with heterogeneous, interacting agents. This major three-volume collection presents the most important papers in the area of complexity in economics.