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Diffeomorphic real-analytic maps and the Jacobian Conjecture

โœ Scribed by M. Chamberland


Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
390 KB
Volume
32
Category
Article
ISSN
0895-7177

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โœฆ 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.


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