On a Transformation of Takens-Argemi-Benoit / Canards from forced Van der Pol oscillator / Albert Einstein: A Biography through The New York Times (Hermann, 2016) [ Back ]

UAB - Dept. Matemàtiques (C1/-128)
Jean-Marc Ginoux
Université du Sud (Toulon)


1- The aim of this work is show that one can deduce the “normalized slow dynamics” associated with a singularly perturbed system of differential equations in $R^3$ and in $R^4$ while using a transformation we call “transformation of Takens-Argemi-Benoit” which enables to find again the generic condition for the existence of canard solutions in the case of pseudo singular points of saddle type.

2- The aim of this work is to propose an alternative method to prove the existence of generic “canards solutions” in four-dimensional singularly perturbed systems with k fast and m slow variables with (k;m)=(3; 1) and (k;m)=(2; 2) while using on the one hand the stability of “folded singularities” of the reduced vector field the definition of which has been introduced recently by Martin Wechselberger and, on the other hand, the stability of “pseudo singular points” of the reduced vector field the definition of which has been introduced by the late Catalan Mathematician José Argémi at the end of the seventies. Application to the forced Van der Pol oscillator will exemplifies this method.

3- This book presents a unique portrait of the famous physicist Albert Einstein entirely based on clippings of a great New-York newspaper: The New York Times. The impressive number of articles about his life and his works offers an original approach to this character. It allows rebuilding, on one hand, almost day to day, the most significant events of his life and, on the other hand, it enables to highlight some of its most intimate traits that appear in the interviews he had granted to this newspaper. It also provides a popularized presentation, devoid of any mathematical development, of his scientific theories (Special and General Relativity and Unified Field Theory) which become thus accessible to the layman. At last, through many unusual and funny anecdotes contained in some unknown articles an unexpected portrait of Einstein is disclosed.