Simultaneous dense and non-dense orbits for certain partially hyperbolic diffeomorphisms
Keyword(s):
Let$g:M\rightarrow M$be a$C^{1+\unicode[STIX]{x1D6FC}}$-partially hyperbolic diffeomorphism preserving an ergodic normalized volume on$M$. We show that, if$f:M\rightarrow M$is a$C^{1+\unicode[STIX]{x1D6FC}}$-Anosov diffeomorphism such that the stable subspaces of$f$and$g$span the whole tangent space at some point on$M$, the set of points that equidistribute under$g$but have non-dense orbits under$f$has full Hausdorff dimension. The same result is also obtained when$M$is the torus and$f$is a toral endomorphism whose center-stable subspace does not contain the stable subspace of$g$at some point.
2014 ◽
Vol 35
(2)
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pp. 412-430
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2016 ◽
Vol 38
(1)
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pp. 384-400
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2017 ◽
Vol 38
(8)
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pp. 2838-2859
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2014 ◽
Vol 36
(1)
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pp. 256-275
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2011 ◽
Vol 54
(4)
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pp. 676-679
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