國外數學名著系列

This volume of the Encyclopaedia is devoted to applications of singularity theory in mathematics and physics. The authors Arnold,Vasilev, Goryunov and Lyashko study bifurcation sets arising in various

functions and Hecke L-functions of an imaginary quadratic field，and various problems on elliptic modular forms. As to the values of Dirichlet L-functions， all previous papers and books reiterate a single old result with a single old method. After a review ofelementary Fourier analysis， the author presents completely new results with new methods. though old results will also be proved. No advanced knowledge of number theory is required up to this point. As applications， new formulas for the second factor ofthe class number of a cyclotomic field will be given. The second half of the book assumes familiarity with basic knowledge ofmodular forms. However，all definitions and facts are clearly stated， and precise references are given. The notion ofnearly holomorphic modular forms is introduced and applied to the determination of the critical values of Hecke L-functions of an imaginary quadratic field. Other notable features of the book are： (1) some new results on classical E

基於對某些重要例子的嚴格分析，《動力系統》概述動力系統及其在複系統和其他領域研究中的意義。著重於動力系統中的不變數，如系統地論述Morse—Conley理論，《動力系統》闡釋了動力系統中的基本數學概念。《動力系統》討論了熵及拓撲、度量、測度、光滑假設中與動力系統有關的概念，以及動力系統與信息理論的某些聯繫。《動力系統》還論述了細胞自動機和隨機布林網絡等特殊例子。