8 citations · 26 across the 22 of their papers we have counts for
22 papers
Margulis Measures on Expanding Foliations: Construction and Rigidity
Jérôme Buzzi, Yi Shi, Fan Yang +1
Given a diffeomorphism preserving a one-dimensional expanding foliation with homogeneous exponential growth, we construct a family of reference measures on each leaf o…
The Teichmüller Space of a 3-Dimensional Anosov Flow
Ruihao Gu, Yi Shi
For a transitive Anosov flow on 3-dimensional closed manifold , we realize its Teichmüller space in the sense of smooth orbit-equivalence classes as a product of two functi…
Lyapunov spectrum rigidity and simultaneous linearization for random Anosov diffeomorphisms
Aaron Brown, Yi Shi
In this paper we study the Lyapunov spectrum rigidity for random walks of expanding maps on unit circle and Anosov diffeomorphisms on -torus . Let $…
Measures of intermediate pressures for geometric Lorenz attractors
Yi Shi, Xiaodong Wang
Pressure measures the complexity of a dynamical system concerning a continuous observation function. A dynamical system is called to admit the intermediate pressure property if for…
Topological and smooth classification of Anosov maps on torus
Ruihao Gu, Yi Shi
In this paper, we give a complete topological and smooth classification of non-invertible Anosov maps on torus. We show that two non-invertible Anosov maps on torus are topological…
-Chain closing lemma for certain partially hyperbolic diffeomorphisms
Yi Shi, Xiaodong Wang
For every , we prove a -orbit connecting lemma for dynamically coherent and plaque expansive partially hyperbolic diffeomorphisms with 1…
Joint integrability and spectral rigidity for Anosov diffeomorphisms
Andrey Gogolev, Yi Shi
Let be an Anosov diffeomorphism whose linearization is irreducible. Assume that is also absolutely partially h…
Rigidity of stable Lyapunov exponents and integrability for Anosov maps
Jinpeng An, Shaobo Gan, Ruihao Gu +1
Let be a non-invertible irreducible Anosov map on -torus. We show that if the stable bundle of is one-dimensional, then has the integrable unstable bundle, if and on…
On multifractal analysis and large deviations of singular-hyperbolic attractors
Yi Shi, Xueting Tian, Paulo Varandas +1
In this paper we study the multifractal analysis and large derivations for singular hyperbolic attractors, including the geometric Lorenz attractors. For each singular hyperbolic h…
A -connecting lemma for Lorenz attractors and its application on the space of ergodic measures
Yi Shi, Xueting Tian, Xiaodong Wang
For every , we prove a -connecting lemma for Lorenz attractors. To be precise, for a Lorenz attractor of a -dimensional ($r\geq…
Centralizers of derived-from-Anosov systems on : rigidity versus triviality
Shaobo Gan, Yi Shi, Disheng Xu +1
In this paper, we study the centralizer of a partially hyperbolic diffeomorphism on which is homotopic to an Anosov automorphism, and we show that either its central…
-Closing lemma for partially hyperbolic diffeomorphisms with 1D-center bundle
Shaobo Gan, Yi Shi
For every , we prove the -closing lemma for general and conservative partially hyperbolic diffeomorphisms with one-dimensional center bun…
Accessibility of derived-from-Anosov systems
Andy Hammerlindl, Yi Shi
This paper shows any non-Anosov partially hyperbolic diffeomorphism on the 3-torus which is homotopic to Anosov must be accessible.
On the density of Birkhoff sums for Anosov diffeomorphisms
Shaobo Gan, Yi Shi, Mingyang Xia
Let f be an Anosov diffeomorphism on a nilmanifold. We consider Birkhoff sums for a Holder continuous observation along periodic orbits. We show that if there are two Birkhoff sums…
A countable partition for singular flows, and its application on the entropy theory
Yi Shi, Fan Yang, Jiagang Yang
In this paper, we construct a countable partition for flows with hyperbolic singularities by introducing a new cross section at each singularity. Such partition forms…
Horizontal diameter of unit spheres with polar foliations and infinitesimally polar actions
Yi Shi
For a singular Riemannian foliation on a Riemannian manifold, a curve is called horizontal if it meets the leaves of perpendicularly. For a singular Rie…
Rigidity of center Lyapunov exponents and -integrability
Shaobo Gan, Yi Shi
Let be a conservative partially hyperbolic diffeomorphism, which is homotopic to an Anosov automorphism on . We show that the stable and unstable bundles of $…
Measures of intermediate entropies for star vector fields
Ming Li, Yi Shi, Shirou Wang +1
We prove that all star vector fields, including Lorenz attractors and multisingular hyperbolic vector fields, admit the intermediate entropy property. To be precise, if is a st…
A robustly transitive diffeomorphism of Kan's type
Cheng Cheng, Shaobo Gan, Yi Shi
We construct a family of partially hyperbolic skew-product diffeomorphisms on that are robustly transitive and admitting two physical measures with intermingled basi…
A chain transitive accessible partially hyperbolic diffeomorphism
Shaobo Gan, Yi Shi
In this paper, we construct a partially hyperbolic skew-product diffeomorphism on , such that is accessible and chain transitive, but not transitive.
The dual foliation of some singular Riemannian foliations
Yi Shi
In this paper, we use the methods of subriemannian geometry to study the dual foliation of the singular Riemannian foliation induced by isometric Lie group actions on a complete Ri…
On the singular hyperbolicity of star flows
Yi Shi, Shaobo Gan, Lan Wen
We prove for a generic star vector field that, if for every chain recurrent class of all singularities in have the same index, then the chain recurrent set of i…