## The equivalence problem in analytic dynamics for 1-resonance

## Speaker

## Abstract

When are two germs of analytic systems conjugate under an analytic change of coordinates in the neighborhood of a singular point? A way to answer is to use normal forms. But there are large classes of dynamical systems for which the change of coordinates to a normal form diverges. Why? In this talk, we will discuss the case of singularities for which the normalizing transformation is 1-summable, thus allowing to provide moduli spaces. We will explain the common geometric features of these singularities, and show that the study of their unfoldings allows understanding the singularities themselves and the geometric obstructions to convergence of the normalizing transformations. We will also present examples of moduli spaces for generic 1-parameter families unfolding such singularities.

**Bio**

Christiane Rousseau got her PhD from the Université de Montréal in 1977. After a postdoc at McGill University, she became professor in the Department of Mathematics and Statistics of the Université de Montréal. Her research field is dynamical systems. She chaired her department from 1993 to 1997. Christiane Rousseau was vice president of the Canadian Mathematical Society for 1995–1997 and then president for 2002–2004. She chaired the Canadian National Committee for 2004–2008 and led two Canadian bids for the International Congress of Mathematicians, ICM 2010 and 2014. Christiane Rousseau was vice president of the International Mathematical Union (IMU) for 2011–2014, and she is a member of the executive committee of the IMU for 2015–2018. She was interim director of CRM for the year 2008–2009. During that period, she started Mathematics of Planet Earth 2013 (MPE 2013) with thirteen North American institutes in mathematical sciences. MPE 2013 grew to the size of an international year under the patronage of UNESCO. For 2015–2017, she is a member of the Scientific Board of the International Basic Sciences Program of UNESCO. Since 2013, she has been a Fellow of the AMS, and she was the recipient of the George Pólya Award in 2014. Christiane Rousseau is very involved in outreach activities, including the magazine Accromath, the organization of public lectures, the organization of math camps, and the training of preservice high school teachers.

Christiane Rousseau was awarded the 2018 Bertrand Russell Prize of the American Mathematical Society in recognition of her many contributions furthering human values and the common good through mathematics. Read more: https://www.ams.org/journals/notices/201804/rnoti-p470.pdf

## Description

**Join us for a reception with light refreshments in WXLR A206 at 3:45pm (before the lecture) and meet our distinguished speaker, professor Christiane Rousseau of the University of Montreal.**

The Basil Nicolaenko Memorial Distinguished Lecture Series in Nonlinear Studies was created to recognize and honor Professor Nicolaenko's exemplary career in mathematics and his passion and intellectual curiosity for teaching nonlinear studies. He was one of the co-founding members of the Center for Nonlinear Studies at the Los Alamos National Laboratory in 1980 and joined the ASU mathematics faculty in 1988 where he was a key leader in the Environmental Fluid Dynamics Group.