Technical Developments of DA on \mathbbT³

2025/09/04 by Zhang, Hangyue
#37C40 #37D25 #37D30 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.04634

Abstract

We constructed a DA on \mathbbT³, which complements the work of Gan, Li, Viana, and Yang (\citeGanLiVianaYang2021) by providing an example of a C^∞-diffeomorphism with partial volume expansion, where dim(E^cs) = 2. In contrast to their work, in \citeGanLiVianaYang2021, they provided an example of a non-invertible embedding in the case dim(E^cs) = 2. The inverse map of the DA we constructed has a mostly expanding center (\citeAnderssonVasquez2018). Using a similar approach, we can also construct a (nontrivial) mixed center (\citeMiCaoYang2017, MiCao2021).

Citations

• SRB measures for partially hyperbolic systems with one-dimensional center subbundles
• Finiteness and Geometric structure of c-cu-States with Maximal u-Entropy
• Physical measures for partially hyperbolic diffeomorphisms with mixed hyperbolicity
• Finiteness of physical measures for diffeomorphisms with multi 1-D centers
• Statistical stability for diffeomorphisms with mostly expanding and mostly contracting centers
• New criterion of physical measures for partially hyperbolic diffeomorphisms
• Measure-theoretical properties of center foliations
• On mostly expanding diffeomorphisms

Related

• Robust minimality of strong foliations for DA diffeomorphisms: cu-volume expansion and new examples
• Many intermingled basins in dimension 3
• A C^∞ closing lemma on torus
• Polynomial growth of the derivative for diffeomorphisms on tori
• A non-dynamically coherent example on \mathbb T³