Search results for " 57M30"

showing 2 items of 2 documents

On proper branched coverings and a question of Vuorinen

2022

We study global injectivity of proper branched coverings from the open Euclidean n$n$-ball onto an open subset of the Euclidean n$n$-space in the case where the branch set is compact. In particular, we show that such mappings are homeomorphisms when n=3$n=3$ or when the branch set is empty. This gives a positive answer to the corresponding cases of a question of Vuorinen. Peer reviewed

Mathematics - Complex VariablesGeneral Mathematicseuklidinen geometriaGeometric Topology (math.GT)Euclidean geometryMathematics - Geometric TopologyMAPSFOS: Mathematics111 MathematicsHigh Energy Physics::ExperimentComplex Variables (math.CV)SETMONODROMY57M12 30C65 57M30
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Aperiodic chain recurrence classes of $C^1$-generic diffeomorphisms

2022

We consider the space of $C^1$-diffeomorphims equipped with the $C^1$-topology on a three dimensional closed manifold. It is known that there are open sets in which $C^1$-generic diffeomorphisms display uncountably many chain recurrences classes, while only countably many of them may contain periodic orbits. The classes without periodic orbits, called aperiodic classes, are the main subject of this paper. The aim of the paper is to show that aperiodic classes of $C^1$-generic diffeomorphisms can exhibit a variety of topological properties. More specifically, there are $C^1$-generic diffeomorphisms with (1) minimal expansive aperiodic classes, (2) minimal but non-uniquely ergodic aperiodic c…

FOS: Mathematics[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS]Dynamical Systems (math.DS)Mathematics - Dynamical Systems37C20 37D30 57M30
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