David Epstein (auth.), Dr. Anthony Manning (eds.)'s Dynamical Systems—Warwick 1974: Proceedings of a Symposium PDF

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By David Epstein (auth.), Dr. Anthony Manning (eds.)

ISBN-10: 3540071849

ISBN-13: 9783540071846

ISBN-10: 3540375252

ISBN-13: 9783540375258

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43 (1974). F. A. Homology classes composed of infinitely many unstable manifolds of a dynamical system. D. SUllivan. A geometric current Y of dimension k in a manifold M is, roughly, any geometric object over which we can integrate k-forms. The current Y is closed provided JY Examples. (a) Any oriented k-dimensional submanifold is a current and it is dcp = 0 for any exact form dcp. closed if it has no boundary. 43 A O-form on M is just a function f:M - R so any finite set [x ' ••• ,x } c M 1 n allows us to integrate f to get Z1 nf(X ).

99 (1974) 154-175. Address. C. Robinson, Department of Mathematics, Northwestern University, Evanston, Illinois 60201, U. A. 24 R. Mane. Absolute and infinitessimal stabil ity. 14. Let M be a compact smooth manifold without boundary and let Diffr(M), r r r ~ 1 be the topological space of C diffeomorphisms with the C topology. t. ) 1 2 O o 1 2 is a Riemannian metric in M. We say that f is infinitessimally stable if I - f :ro(TM) _ ,o(TM) is surjective (ro(TM) = Banach space of continuous * 1 Franks and Guckenheimer [2J proved that a C -absolutely sections of TM).

What can be said if So is Anosov or a general Axiom A system ? In particular, find conditions in the boundary of an Anosov or Axiom A conjugacy class that define a codimension one submanifold of Diffr(M). S If f , f E M - S are isotopic is there a C arc, s ~ 0, in 1 2 Diffr(M) connecting f and f~ having only finitely or countably many bifurcation 1 points? This is false in S , an obstruction being the rotation number. Question 5. An arc S is structurally stable if any nearby arc 1'1 is equivalent to S in the following sense.

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Dynamical Systems—Warwick 1974: Proceedings of a Symposium Held at the University of Warwick 1973/74 by David Epstein (auth.), Dr. Anthony Manning (eds.)

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