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Ergodic attractors. (English) Zbl 0684.58008
Authors’ 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.
Reviewer’s comment: The paper constitutes a topic of interest mainly to a very particular school of (soft) mathematics. In particular it redefines usual notions, like for example ‘ergodicity’, so that the new definitions would fit various results of that school. In such a way, the existence of ‘ergodic attractors’ becomes possible, and some of their properties can be easily described. Since such ‘ergodic attractors’ have nothing in common with what one would expect in complex natural dynamic phenomena, for example in a physical turbulence, general, and especially applied readers may safely ignore this paper.
Reviewer: J.Gumowski

MSC:
58D15 Manifolds of mappings
58D99 Spaces and manifolds of mappings (including nonlinear versions of 46Exx)
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