Welcome to My Webpage!

Name in Chinese
Family Name: FU 
Forenames: Xinchu  
Place of Birth: Hubei, China 

BSc, MSc in Maths (Wuhan) 
PhD in Maths (Exeter, UK)
Professor of Applied Maths

Mr FU Xin Chu Department of Mathematics  
Shanghai University  
Shanghai 200444 
P. R. CHINA  

Tel: +86-21-66133902 
Fax: +86-21-66133292 
xcfu@mail.shu.edu.cn 

Research Interests

I am interested in the theory, methods and applications of Symbolic Dynamics, Topological Dynamics and Infinite-Dimensional Dynamical Systems. Currently, I am working on dynamics of some discontinuous maps, such as linear torus maps, piecewise isometries...

Recent Research Project

The Overflow Oscillation (-Picture from Peter)The EPSRC funded project (Feb. 1999 - March 2002): ``Dynamics of Discontinuous Area-preserving Maps and Signal Processing'' (Principal investigator: Dr Peter Ashwin).

The aim of this project is to develop fundamental theory for the dynamics of discontinuous conservative maps and apply this to problems in signal processing that have this structure, notably overflow oscillations of digital filters and sigma-delta modulators.

The project focus on new dynamical, bifurcational, topological and measure-theoretic effects due to presence of discontinuities in systems where all Lyapunov exponents are zero. It examines similar systems (eg polygonal billiards) and explores ways of modelling such systems using symbolic dynamics and subshifts of infinite type.

Selected Publications

Peter Ashwin and Xin-Chu Fu, On the geometry of orientation preserving planar piecewise isometries. J. of Nonl. Science, 12 (2002) 207-240.

Peter Ashwin, Xin-Chu Fu and J. Terry, Riddling of invariant sets for some discontinuous maps preserving Lebesgue measure. Nonlinearity, 15 (2002) 633-645.

Jinqiao Duan and Xin-Chu Fu, Time-periodically forced amplitude evolution in spatially extended nonlinear systems, Appl. Math. & Computation, 127 (2002) 215-219.

Peter Ashwin and Xin-Chu Fu, On the dynamics of some nonhyperbolic area-preserving piecewise linear maps. in "Mathematics in Signal Processing V", Oxford Univ. Press IMA Conference Series, 2002.

Xin-Chu Fu, Weiping Lu, Peter Ashwin and Jinqiao Duan, Symbolic representations of iterated maps, Top. Meth. Nonl. Anal., 18 (2001) 119-147.

Peter Ashwin and Xin-Chu Fu, Tangencies in invariant circle packings for certain planar piecewise isometries are rare, Dynamical Systems, 16 (2001) 333-345.

Peter Ashwin, Jonathan Deane and Xin-Chu Fu, Dynamics of a bandpass sigma-delta modulator as a piecewise isometry,in Proceedings of ISCAS'2001, Sydney, Australia, 2001, III: 811-814.

Xin-Chu Fu, Yibin Fu, Jinqiao Duan, and Robert S. MacKay, Chaotic properties of subshifts generated by a non-periodic recurrent orbit, Intern. J. of Bif. & Chaos, 10 (2000) 1067-1073.

Hongjun Gao, Jinqiao Duan and Xin-Chu Fu, Almost periodic passive tracer dispersion, J. Math. Anal. & Appl., 247 (2000) 300-308.

Peter Ashwin, Xin-Chu Fu, Takashi Nishikawa and Karol Zyczkowski, Invariant sets for discontinuous parabolic area-preserving torus maps, Nonlinearity, 13 (2000) 819-835.

Xin-Chu Fu and Jinqiao Duan, Infinite-dimensional linear dynamical systems with chaoticity, J. of Nonl. Science, 9 (1999) 197-211.

Jinqiao Duan, Xin-Chu Fu, Pei-De Liu and Anthony Manning, On a linear chaotic quantum harmonic oscillator, Applied Math. Lett., 12 (1999) 15-19.

Jinqiao Duan, Xin-Chu Fu, Eric Lowenstein and Janpou Nee, Dynamical difference between nonlocal and local Burgers equations, in Proc. of the 3rd Int. Conference on Nonl.Mech., ICNM-III, Shanghai, China, August 1998, 630-633.

Xin-Chu Fu, Criteria for a general continuous self-map to have chaotic sets, Nonl. Anal. TMA, 26 (1996) 329-334.

Xin-Chu Fu and You-Zhong Guo, Symbolic dynamics with a countable alphabet, session talk given at {\it the 2nd Int. Conference on Nonl. Mech.}, Beijing, China, August 23-26, 1993. And in Applied Math. & Mech., Wei-Zang Chien 80th Anniversary Volume, 1993, 76-85.

Xin-Chu Fu and Huan-Wen Chou, Chaotic behavior of the general symbolic dynamics, Applied Math. & Mech., 13 (1992) 117-123.

Xin-Chu Fu and Kai-Hua Xu, The Conley index and bifurcation points, Nonl. Anal. TMA, 19 (1992) 1137-1142.

Xin-Chu Fu, Huan-Wen Chou and Kai-Hua Xu, Bifurcations, Chaos, and Symbolic Dynamics, Wuhan University Press, Wuhan, China, 1993.

Email: xcfu@mail.shu.edu.cn  Last Modified: 12 Dec. 2002