Diffeomorphic real-analytic maps and the Jacobian Conjecture

✍ Scribed by M. Chamberland

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 390 KB
• Volume: 32
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(00)00167-9

✦ Synopsis

It is shown that if the real-analytic map f(x) : Ill2 + BP2 has a Jacobian matrix whose eigenvaluee are always both one, then the map ls a diffeemorphism. An explicit form of the inverse ls given. The proof relies on a result which says that the only global solutions to the quasi-linear partial differential equation (cos u)us -(sin u)uV = 0 are constant functions. The main result is put into a context concerning the Jacobian Conjecture.