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Oct 13, 2010 at 15:18 answer added Stephen Miller timeline score: 1
Sep 9, 2010 at 1:39 answer added Martin timeline score: 2
Jun 10, 2010 at 2:57 comment added Steve Huntsman Wish I could accept both answers, and Deane's comments as well. Thanks all!
Jun 10, 2010 at 2:56 vote accept Steve Huntsman
Jun 9, 2010 at 17:04 comment added Steve Huntsman ...continuing...but now it seems that I have any right to expect the situation to be anywhere near my hopes.
Jun 9, 2010 at 17:02 comment added Steve Huntsman @Deane--Very good point, I (wasn't aware of and) hadn't considered the uniqueness of the diffeomorphism, esp. vs. the conformal rescaling....In the application I have in mind, $f$ is Anosov and the only natural initial choice of metric I can think of would be an Anosov (by normalization, not necessarily Lyapunov) metric. But this is not (unique as far as I know or) $f$-invariant, even assuming $f$ is conservative. But what I mean by "natural" can be somewhat clarified in the ideal case: there'd be some unique way to pick out a distinguished metric giving rise to the $f$-invariant measure.
Jun 9, 2010 at 16:39 comment added Deane Yang Why is pulling back $g$ using a diffeomorphism constructed using Moser's trick more natural or better than just changing $g$ by a conformal factor? Given the original metric $g$, the conformal factor is uniquely determined (which fits my definition of "natural"), but the diffeomorphism that pulls back $\nu$ to $\nu_f$ is far from unique.
Jun 9, 2010 at 13:10 comment added Steve Huntsman I thought the pullback suggested by the Moser theorem in coudy's answer was pretty close to what I had in mind.
Jun 9, 2010 at 12:00 comment added Deane Yang Steve, as I comment below, there are many different metrics with a given measure. All you have to do is start with arbitrary metric $g$ with volume measure $\mu$ and define $g_f = g(\nu/\mu)^{2/n}$. Again, what do you mean by "natural"?
Jun 8, 2010 at 21:12 comment added Steve Huntsman So-called conservative diffeomorphisms preserve a natural Riemannian measure. So my question could be rephrased as: given a conservative $f$ and its preserved measure $\nu$, is there a natural metric $g_f$ whose measure is also $\nu$?
Jun 8, 2010 at 21:04 answer added coudy timeline score: 6
Jun 8, 2010 at 20:48 answer added rpotrie timeline score: 3
Jun 8, 2010 at 20:38 comment added Steve Huntsman @Will--For background: arxiv.org/pdf/0804.0167
Jun 8, 2010 at 20:36 comment added Steve Huntsman @Deane--The original metric is just mentioned to distinguish it from the putative $g_f$.
Jun 8, 2010 at 19:56 comment added Deane Yang What is the role of the original metric $g$ in your question? And what is the meaning of "natural"?
Jun 8, 2010 at 19:52 history asked Steve Huntsman CC BY-SA 2.5