On Tuesday, November 6th, at 5pm in room 630, starts a series of lectures on the topic “Bifurcation in the Theory of Catastrophes“. The lecturer will be Prof. Susumu Tanabe from the Moscow Institute of Physics and Technology (MIPT).
The purpose of this lecture series is to introduce the geometric basis for studying bifurcation phenomena through the use of the theory of catastrophes. Although mathematical analysis of real and complex functions allows us to examine only smooth and continuous processes, the theory of catastrophes offers a universal method for investigating abrupt transitions, discontinuities, and sudden qualitative changes through the synthesis of topology, analysis, and commutative algebra.
This theory is applicable to various fields of both natural and social science, such as cardiology, embryology, optics, optimization problems, cosmology, gas dynamics, the sociology of revolutions, and economic theories of market collapse. Its foundation lies in the study of topological changes within the phase portrait of a dynamic system.
The beginning of the course will focus on explaining the role of parameter changes in the topology bifurcation of a manifold. We welcome suggestions from listeners for mathematical models to study (differential, functional, equations for multiple functions, etc.) depending on parameters. The course is designed for third-year and above students, undergraduates, and graduates who are familiar with mathematical analysis of functions in multiple variables.
References
V. A. Arnold, The Theory of Catastrophes (links to scientific articles can be found in this book). M, 1990.
N. G. Pavlova and A. O. Remizov, An Introduction to Singularity Theory. MIPT, 2021.
M. Golubitsky and V. Guillemin, Stable Transformations and Their Properties (translated by A. G. Kushnirenko and edited by V. I. Arnold). M. 1977.
R. Volke, Structural Stability and Morphogenesis: A Review of the General Theory of Models. Addison-Wesley, 1989.
J. Guckenheimer and P. Holmes’ book “Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields” was published by Springer in 1983.