A note on expansiveness and hyperbolicity for generic geodesic flows

DOI10.1007/S11040-018-9271-7zbMath1395.37018arXiv1808.04333OpenAlexW3105282885WikidataQ128739758 ScholiaQ128739758MaRDI QIDQ1664461

Mário Bessa, Fabio Berra

Publication date: 27 August 2018

Published in: Proceedings of the American Mathematical Society, Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.04333

zbMATH Keywords

maximal operatorsgeodesic flowMuckenhoupt weightsresidual setAnosov flowexpansivenessYoung functions

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Maximal functions, Littlewood-Paley theory (42B25) Generic properties, structural stability of dynamical systems (37C20) Geodesic flows in symplectic geometry and contact geometry (53D25) Dynamical systems of geometric origin and hyperbolicity (geodesic and horocycle flows, etc.) (37D40)

Related Items (10)

From \(A_1\) to \(A_{\infty}\): new mixed inequalities for certain maximal operators ⋮ Sawyer-type inequalities for Lorentz spaces ⋮ Improvements on Sawyer type estimates for generalized maximal functions ⋮ Mixed weak type inequalities for the fractional maximal operator ⋮ Mixed inequalities for operators associated to critical radius functions with applications to Schrödinger type operators ⋮ A sparse approach to mixed weak type inequalities ⋮ Mixed inequalities of Fefferman-Stein type for singular integral operators ⋮ Weak and strong type estimates for the multilinear pseudo-differential operators ⋮ Expansiveness and hyperbolicity in convex billiards ⋮ Some mixed weak type inequalities

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geodesic flows with positive topological entropy, twist maps and hyperbolicity
• Shadowing, expansiveness and specification for \(C^1\)-conservative systems
• A generic incompressible flow is topological mixing
• Persistently expansive geodesic flows
• On the creation of conjugate points
• Genericity of geodesic flows with positive topological entropy on \(S^2\)
• Closing geodesics in \(C^1\) topology
• Mixed weak estimates of Sawyer type for fractional integrals and some related operators
• The \(C^0\) general density theorem for geodesic flows
• On shadowing and hyperbolicity for geodesic flows on surfaces
• Proof of an extension of E. Sawyer's conjecture about weighted mixed weak-type estimates
• Generic properties of geodesic flows
• Expansive one-parameter flows
• The C¹ Closing Lemma, including Hamiltonians
• A Weighted Weak Type Inequality for the Maximal Function
• Type des points fixes des difféomorphismes symplectiques de $\bbfT{}\sp n\times{}\bbfR{}\sp n$
• Characterization of Subsets of Rectifiable Curves in R ⁿ
• Homoclinic points near elliptic fixed points

This page was built for publication: A note on expansiveness and hyperbolicity for generic geodesic flows