This work focuses on the preservation of attractors and saddle points of ordinary differential equations under discretisation. In the 1980s, key results for autonomous ordinary differential equations were obtained – by Beyn for saddle points and by Kloeden & Lorenz for attractors. One-step numerical schemes with a constant step size were considered, so the resulting discrete time dynamical system was also autonomous. One of the aims of this book is to present new findings on the discretisation of dissipative nonautonomous dynamical systems that have been obtained in recent years, and in particular to examine the properties of nonautonomous omega limit sets and their approximations by numerical schemes – results that are also of importance for autonomous systems approximated by a numerical scheme with variable time steps, thus by a discrete time nonautonomous dynamical system.
Vaysse, Charlotte; Chantalat, Elodie; Beyne-Rauzy, Odile; Morineau, Louise; Despas, Fabien; Bachaud, Jean-Marc; Caunes, Nathalie; Poublanc, Muriel; Serrano, Elie; Bugat, Roland; Rougé Bugat, Marie-Eve; Fize, Anne-Laure
traditional classroom of 25 students, online education became more effective when there were more than 950 participants. SPOCs improved the management of oncology patients. This new digital learning technique is an attractive concept to integrate into teaching practice. It offered optimal propagation of information and met the students' expectations. ©Charlotte Vaysse, Elodie Chantalat, Odile Beyne-Rauzy, Louise Morineau, Fabien Despas, Jean-Marc Bachaud, Nathalie Caunes, Muriel Poublanc, Elie Serrano, Roland Bugat, Marie-Eve Rougé Bugat, Anne-Laure Fize. Originally published in JMIR Medical Education (http://mededu.jmir.org), 05.03.2018.