# J.P. Jouanolou's Equations de Pfaff algébriques PDF

By J.P. Jouanolou

ISBN-10: 0387092390

ISBN-13: 9780387092393

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Extra info for Equations de Pfaff algébriques

Sample text

We claim t h at if X e dFflG and f'(X)*0, then X is not on the inner boundary of F. To see this, pick a small open disc centered at f(X), say U, so t h a t one can find an analytic function g on U satisfying Xeg(U)cG, and g(f(w))=w for all weg(U). regions U_ and U The circle centered where at the origin with radius £ divides U into two 28 MILLER, OLIN AND THOMSON U_ = {\p\e}n\J. and Clearly, g(U_)cC NF and X e dg(U_). Hence, the claim is established. Now, using the claim, we see t h a t if \edFC\G 6, the set int A(X,6) N F contains an arc and f'(X)*0, then, for sufficiently whose diameter exceeds 8/2.

Suppose the last assertion is false. Then there exist a closed subset K of F and e > 0 such t h a t /i(K)>0 and e < h < l - e on K. Let G s £ ~ l r | K*n^ * t h a t is, for each s in C(K ) J sd

Such t h a t for z ^ E If version Let of the main conclusion in Theorem 48 actually /x be a measure on dG and let feC(M), then there exist closed v subsets holds for be a minimal measure with {E } of dG with nE -*>1 and ,