A note on partially hyperbolic attractors: Entropy conjecture and SRB measures
Peidong Liu Kening Lu
Discrete & Continuous Dynamical Systems - A 2015, 35(1): 341-352 doi: 10.3934/dcds.2015.35.341
In this note we show that, for a class of partially hyperbolic $C^r$ ($r \geq 1$) diffeomorphisms, (1) Shub's entropy conjecture holds true; (2) SRB measures exist as zero-noise limits.
keywords: Partially hyperbolic attractors random perturbations. entropy conjecture SRB measures
Topological stability of hyperbolic sets of flows under random perturbations
Qiuxia Liu Peidong Liu
Discrete & Continuous Dynamical Systems - B 2010, 13(1): 117-127 doi: 10.3934/dcdsb.2010.13.117
In this paper we consider $C^{0}$ random perturbations of a hyperbolic set of a flow. We show that the hyperbolic set is structurally semi-stable under such perturbations.
keywords: hyperbolic set $C^{0}$ random perturbation. flow
Existence of SRB measures for a class of partially hyperbolic attractors in banach spaces
Zeng Lian Peidong Liu Kening Lu
Discrete & Continuous Dynamical Systems - A 2017, 37(7): 3905-3920 doi: 10.3934/dcds.2017164

In this paper, we study the existence of SRB measures for infinite dimensional dynamical systems in a Banach space. We show that if the system has a partially hyperbolic attractor with nontrivial finite dimensional unstable directions, then it has an SRB measure.

keywords: SRB measure infinite dimensional dynamical systems partial hyperbolicity chaotic behavior

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