Fourier Coefficients, Lyapunov Exponents, Invariant Measures and Chaos

• Main Authors: Huan-Hsun Hsu, 許奐勛
• Other Authors: Jonq Juang
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/53092886363543993990

碩士 === 國立交通大學 === 應用數學系所 === 94 === A complex and unpredictable frequency spectrum of a signal has long been seen in physics and engineering as an indication of a chaotic signal. The first step to understand such phenomenon mathematically was taken up by Chen, Hsu, Huang and Roque-Sol. In particular, they look for possible connections between chaotic dynamical systems and the behavior of its Fourier coefficients. Among other things, they found variety of sufficient conditions on the Fourier coefficients of the -th iterate of an interval map , for which the topological entropy of is positive. In this thesis, we explore the relationship between the Fourier coefficients of an interval map and its Lyapunov exponent and invariant measure. Specifically, the relationships between those three quantities of two family of interval maps, piecewise linear maps admitting a Markov partition and quadratic family, are considered.