Proper minimal sets on compact connected 2-manifolds are nowhere dense

DOI10.1017/S0143385707000740zbMath1171.37008OpenAlexW1982244490MaRDI QIDQ3509958

Ľubomír Snoha, Sergei I. Trofimchuk, Sergiǐ F. Kolyada

Publication date: 25 June 2008

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385707000740

zbMATH Keywords

minimalitytwo-dimensional manifoldnowhere densemonotone-light decomposition

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces (37E30) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (9)

Dynamics of inner mappings ⋮ Unnamed Item ⋮ Minimal sets on continua with a dense free interval ⋮ On minimal homeomorphisms and non-invertible maps preserving foliations ⋮ Minimal sets of fibre-preserving maps in graph bundles ⋮ The life and mathematics of Sergiĭ Kolyada ⋮ Minimal extensions of flows with amenable acting groups ⋮ Minimal sets in compact connected subspaces ⋮ Construction of minimal non-invertible skew-product maps on 2-manifolds

Cites Work

• A point distal transformation of the torus
• An index theorem for the homeomorphisms of the plane near a fixed point
• Fixed points for iterates
• Monontone transformations of two-dimensional manifolds
• The existence of periodic points
• ON MINIMAL SETS IN DYNAMICAL SYSTEMS
• On almost one-to-one maps
• Minimal Sets on Graphs and Dendrites
• On minimal maps of 2-manifolds
• The Construction of Minimal Discrete Flows
• Pointwise-recurrent graph maps
• Orbit-closure decompositions and almost periodic properties

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