Hyperbolicity and Rigidity for Fibred Partially Hyperbolic Systems

Chakraborty，Sankhadip1,2; Viana，Marcelo1

2024

10.1007/s10884-023-10343-6

Journal of Dynamics and Differential Equations   影响因子和分区

1040-7294

1572-9222

Every volume-preserving accessible centre-bunched fibred partially hyperbolic system with 2-dimensional centre either (a) has two distinct centre Lyapunov exponents, or (b) exhibits an invariant continuous line field (or pair of line fields) tangent to the centre leaves, or (c) admits a continuous conformal structure on the centre leaves invariant under both the dynamics and the stable and unstable holonomies. The last two alternatives carry strong restrictions on the topology of the centre leaves: (b) can only occur on tori, and for (c) the centre leaves must be either tori or spheres. Moreover, under some additional conditions, such maps are rigid, in the sense that they are topologically conjugate to specific algebraic models. When the system is symplectic (a) implies that the centre Lyapunov exponents are non-zero, and thus the system is (non-uniformly) hyperbolic.

Holonomy map Hyperbolicity Partially hyperbolic system Rigidity Symplectic diffeomorphism Volume-preserving diffeomorphism

SCI

英语

其他

2-s2.0-85182854268

Scopus

1.IMPA - Instituto de Matemática Pura e Aplicada,Rio de Janeiro,Estrada Dona Castorina 110,22460-320,Brazil
2.Department of Mathematics,Southern University of Science and Technology,Shenzhen,1088 Xueyuan Avenue,518055,China

Chakraborty，Sankhadip,Viana，Marcelo. Hyperbolicity and Rigidity for Fibred Partially Hyperbolic Systems[J]. Journal of Dynamics and Differential Equations,2024.

Chakraborty，Sankhadip,&Viana，Marcelo.(2024).Hyperbolicity and Rigidity for Fibred Partially Hyperbolic Systems.Journal of Dynamics and Differential Equations.

Chakraborty，Sankhadip,et al."Hyperbolicity and Rigidity for Fibred Partially Hyperbolic Systems".Journal of Dynamics and Differential Equations (2024).