Surgery for partially hyperbolic dynamical systems II. Blow-up of a complex curve
Sign Up to like & getrecommendations! Published in 2019 at "Mathematische Zeitschrift"
DOI: 10.1007/s00209-020-02681-8
Abstract: In this paper we use the blow-up surgery introduced in [ 1 ] to produce new higher dimensional partially hyperbolic flows. The main contribution of the paper is the slow-down construction which accompanies the blow-up construction… read more here.
Keywords: hyperbolic flows; blow; partially hyperbolic; complex curve ... See more keywords
Classification of partially hyperbolic surface endomorphisms
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DOI: 10.1007/s10711-022-00684-9
Abstract: We show that in the absence of periodic centre annuli, a partially hyperbolic surface endomorphism is dynamically coherent and leaf conjugate to its linearisation. We proceed to characterise the dynamics in the presence of periodic… read more here.
Keywords: partially hyperbolic; surface endomorphisms; hyperbolic surface; classification partially ... See more keywords
Quasi-shadowing and limit quasi-shadowing for quasi-partially hyperbolic strings of flows
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DOI: 10.1016/j.jde.2020.07.030
Abstract: Abstract In this paper, we study the quasi-shadowing property for quasi-partially hyperbolic δ-pseudo-orbit made by quasi-partially hyperbolic strings. We also investigate the corresponding L p , limit and asymptotic quasi-shadowing properties. As an application, we… read more here.
Keywords: partially hyperbolic; limit; quasi shadowing; hyperbolic strings ... See more keywords
Cocycle rigidity of partially hyperbolic abelian actions with almost rank-one factors
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DOI: 10.1017/etds.2017.119
Abstract: We extend the recent progress on the cocycle rigidity of partially hyperbolic homogeneous abelian actions to the setting with rank-one factors in the universal cover. The method of proof relies on the periodic cycle functional… read more here.
Keywords: cocycle rigidity; abelian actions; partially hyperbolic; rank one ... See more keywords
Physical measures for certain partially hyperbolic attractors on 3-manifolds
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DOI: 10.1017/etds.2017.24
Abstract: In this work, we analyze ergodic properties of certain partially hyperbolic attractors whose central direction has a neutral behavior; the main feature is a condition of transversality between the projections of unstable leaves, projecting through… read more here.
Keywords: attractors manifolds; measures certain; hyperbolic attractors; physical measures ... See more keywords
Volume lemmas and large deviations for partially hyperbolic endomorphisms
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DOI: 10.1017/etds.2019.63
Abstract: We consider partially hyperbolic attractors for non-singular endomorphisms admitting an invariant stable bundle and a positively invariant cone field with non-uniform cone expansion at a positive Lebesgue measure set of points. We prove volume lemmas… read more here.
Keywords: lemmas large; partially hyperbolic; measure; volume lemmas ... See more keywords
Classification of partially hyperbolic diffeomorphisms under some rigid conditions
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DOI: 10.1017/etds.2020.85
Abstract: Abstract Consider a three-dimensional partially hyperbolic diffeomorphism. It is proved that under some rigid hypothesis on the tangent bundle dynamics, the map is (modulo finite covers and iterates) an Anosov diffeomorphism, a (generalized) skew-product or… read more here.
Keywords: classification partially; hyperbolic diffeomorphisms; partially hyperbolic; diffeomorphisms rigid ... See more keywords
Unstable entropies and dimension theory of partially hyperbolic systems
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DOI: 10.1088/1361-6544/ac3dcb
Abstract: In this paper we define unstable topological entropy for any subsets (not necessarily compact or invariant) in partially hyperbolic systems as a Carathéodory–Pesin dimension characteristic, motivated by the work of Bowen and Pesin etc. We… read more here.
Keywords: partially hyperbolic; unstable topological; dimension theory; hyperbolic systems ... See more keywords