Jacobian Conjecture and Nilpotent Mappings

1998/03/29 by Вик. С. Куликов, Vik. S. Kulikov, Kulikov, Vik. S.
Mathematics · #14J99 (Primary) #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J99

paper · pdf · doi:10.48550/arxiv.math/9803143

10 pages, LaTeX2e

arxiv created 1998/03/29 · openalex publication_date 1998/03/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove the equivalence of the Jacobian Conjecture (JC(n)) and the Conjecture on the cardinality of the set of fixed points of a polynomial nilpotent mapping (JN(n)) and prove a series of assertions confirming JN(n).

Related

• A new class of Nilpotent Jacobians in any dimension
• The Jacobian conjecture and injectivity conditions
• On mappings with Jacobian one
• The Jacobian Conjecture: Approximate roots and intersection numbers
• Some polynomial maps with Jacobian rank two or three