I. Gumowski and a Toulouse research group in the ``prehistoric'' times of chaotic dynamics (Q2712268)

This is a survey of the works on nonlinear dynamics carried out by members of the Toulouse research group, often under a strong influence of Prof. Gumowski. It covers the period, which the author calls the ``prehistoric times of chaotic dynamics'', i.e. from the end of the 1950's till 1976. The results are mainly related to iterations of two-dimensional dissipative and conservative maps, basins of attractors, one-dimensional maps, bifurcations, especially bifurcations near resonant fixed points. The paper contains a lot of examples, describes several applications to nonlinear electronic circuits and has an extensive bibliography. NEWLINENEWLINEThe following sections are included:NEWLINENEWLINE-- Introduction. Birth of the group. Approach of dynamic problems (processes)NEWLINENEWLINE-- First Contact with Complex Dynamics (1958--1960)NEWLINENEWLINE-- Basin Boundaries of Two-Dimensional Noninvertible Maps (1963--1975)NEWLINENEWLINE-- Genesis of the resultsNEWLINENEWLINE-- First example: fractal organization of non connected basins (1968--1969)NEWLINENEWLINE-- Second example: fractalization of a basin boundary (1968--1969)NEWLINENEWLINE-- Third example: fractal organization with a multiply connected basin (1973)NEWLINENEWLINE-- Chaotic Attractors of Two-Dimensional Noninvertible Maps (1968--1975)NEWLINENEWLINE-- Maps far from the conservative caseNEWLINENEWLINE-- Perturbation of conservative casesNEWLINENEWLINE-- Normal Forms for Resonant Bifurcations (1969--1974)NEWLINENEWLINE-- Two-Dimensional Conservative Maps (1970--1975)NEWLINENEWLINE-- Framework of the researchNEWLINENEWLINE-- Study of unbounded quadratic mapNEWLINENEWLINE-- Asymptotic propertiesNEWLINENEWLINE-- BifurcationsNEWLINENEWLINE-- Study of unbounded cubic mapNEWLINENEWLINE-- Study of map with bounded nonlinearityNEWLINENEWLINE-- Study of almost conservative maps (1973--1976)NEWLINENEWLINE-- Study of One-Dimensional Non-invertible Maps (from 1972)NEWLINENEWLINE-- Basis of the studyNEWLINENEWLINE-- The box-within-the-box bifurcation (or embedded boxes) structureNEWLINENEWLINE-- ConsequencesNEWLINENEWLINE-- ApplicationsNEWLINENEWLINE The International Colloquium ``Transformations Ponctuelles et leurs Applications'' (Point mapping and Applications): Two Exhibitions of Chaotic Images (1973 and 1975)NEWLINENEWLINE-- ConclusionNEWLINENEWLINE-- ReferencesNEWLINENEWLINEFor the entire collection see [Zbl 0958.00013].