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Transactions of the American Mathematical Society

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Ergodic attractors

Authors: Charles Pugh and Michael Shub
Journal: Trans. Amer. Math. Soc. 312 (1989), 1-54
MSC: Primary 58F12; Secondary 28D05, 58F11, 58F15, 58F18
MathSciNet review: 983869
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Abstract: Using the graph transform method, we give a geometric treatment of Pesin's invariant manifold theory. Beyond deriving the existence, uniqueness, and smoothness results by Fathi, Herman, and Yoccoz our method allows us to do four things: optimally conserve smoothness, deal with endomorphisms, prove absolute continuity of the Pesin laminations, and produce ergodic attractors.

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