# American Institute of Mathematical Sciences

December  2003, 2(4): 425-445. doi: 10.3934/cpaa.2003.2.425

## Factor analysis of nonlinear mappings: p-regularity theory

 1 Control and Dynamical Systems 107-81, California Institute of Technology, Pasadena, CA 91125, United States 2 Computing Center of the Russian Academy of Sciences, Vavilova 40, Moscow, GSP-1, Russian Federation

Received  December 2002 Revised  June 2003 Published  October 2003

The paper presents recent advances in $p$-regularity theory, which has been developing successfully for the last twenty years. The main result of this theory gives a detailed description of the structure of the zero set of an irregular nonlinear mapping. We illustrate the theory with an application to degenerate problems in different fields of mathematics, which substantiates the general applicability of the class of $p$-regular problems. Moreover, the connection between singular problems and nonlinear mappings is shown. Amongst the applications, the structure of $p$-factor-operators is used to construct numerical methods for solving degenerate nonlinear equations and optimization problems.
Citation: Jerrold E. Marsden, Alexey Tret'yakov. Factor analysis of nonlinear mappings: p-regularity theory. Communications on Pure & Applied Analysis, 2003, 2 (4) : 425-445. doi: 10.3934/cpaa.2003.2.425
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