PERSONAL INFORMATION
Name: Xuanji HOU, Associate Professor
Address: School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China
E-mail:hxj@mail.ccnu.edu.cn
Phone: 86-15307198717
EDUCATION
Ph.D. Mathematics, Nanjing University, 2005-2008. Dissertation: Quasi-Periodic Linear Skew-Product Systems. Advisor: Professor Jiangong You.
M.A. Mathematics, Nanjing University, 2002-2005.
B.A. Mathematics, Anqing Normal College, 1998-2002.
RESEARCH INTERESTS AND CURRENT RESEARCH WORKS
Reducibility Problems in Dynamical Systems
We have done some research on reducibility problems of quasi-periodic linear systems. The main technique we used are KAM and Renormalization. We have proved by an adapted KAM iteration that the almost reducibility of analytic quasi-periodic ODE with two frequecy, provided that the frequency is rational independent and the coefficient is sufficiently close to some constant. Such a result has some important application in one-dimensional quasi-periodic Shrodinger operator theory. We have also considered some rigidity problems of the reducibility of analytic quasi-periodic linear systems and proved some results by using KAM and Renormalization.
Currently, we go on to study some related problems. We extending our rigidity result of the reducibility of analytic quasi-priodic linear systems to Gevrey case. We are considering the reducibility problems of linear systems beyond quasi-periodic. We are also interested in the linearization problems of some non-linear systems.
ACADEMIC VISITS
April 1 - April 7, 2012：Mathematisches Forschungsinstitut Oberwolfach, Germany
November 12-November 16, 2012: Centre International de Rencontre Mathematiques,France
March 7-March 20, 2013: Chinese University of HongKong, Hongkong
