Minimal extensions in smooth dynamics
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Dátum
2024
Autori
Názov časopisu
ISSN časopisu
Názov zväzku
Vydavateľ
Springer Nature : Viedeň
ISBN
ISSN
0026-9255
1436-5081
1436-5081
Abstrakt
A classical result of Fathi and Herman from 1977 states that a smooth compact connected manifold without boundary admitting a locally free action of a 1-torus, respectively, an almost free action of a 2-torus, admits a minimal diffeomorphism, respectively, a minimal flow. In the first part of our paper we study the existence of locally free and almost free actions of tori on homogeneous spaces of compact connected Lie groups, thus providing new examples of spaces admitting minimal diffeomorphisms or flows. In the second part we combine the ideas of Fathi and Herman with our recent ideas to study the existence of minimal skew products over certain minimal flows with general connected Lie groups as acting groups. Our results apply to so called flows with free cycles. In the last part of our work we study the existence of free cycles in homogeneous flows.
Popis
In: Monatshefte für Mathematik. Viedeň : Springer Nature, 2024. ISSN 0026-9255. Vol. 4, no. 204 (2024), pp. 783-838.
Kľúčové slová
minimálny tok, minimálne rozšírenie
Výstup z projektu
VEGA 1/0158/20 Minimálnosť a chaos v dynamických systémoch
Citácia
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CC BY Creative Commons Attribution 4.0. International
info:eu-repo/semantics/openAccess
info:eu-repo/semantics/openAccess