2019/04/10 by Elżbieta Adamus, Adamus, Elżbieta, Paweł Bogdan +1
Mathematics · #Advanced Differential Equations and Dynamical Systems #Mathematical Dynamics and Fractals #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.1904.05138
In our previous paper an effective algorithm for inverting polynomial automorphisms was proposed. Also the class of Pascal finite polynomial automorphisms was introduced. Pascal finite polynomial maps constitute a generalization of exponential automorphisms to positive characteristic. In this note we explore properties of the algorithm while using Segre homotopy and reductions modulo prime number. We give a method of retrieving an inverse of a given polynomial automorphism F with integer coefficients form a finite set of the inverses of its reductions modulo prime numbers. Some examples illustrate effective aspects of our approach.