Brief Introduction of HOU, Xuanji -华中师范大学数学学院中文站

Brief Introduction of HOU, Xuanji

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Personal Introduction

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 Field?

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 Visit

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

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Brief Introduction of HOU, Xuanji

Chinese Version (中文版)