Geodesic
Topological equicontinuity and topological uniform rigidity for dynamical system
Filomat, Tome 37 (2023) no. 20, p. 6813

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DOI

In this paper, we study topological equicontinuity, topological uniform rigidity and their properties. For a dynamical system, on a compact, T3 space, we study relations among the set of recurrent points of the map, the set of non-wandering points of the map and the intersection of the range sets of all iterations of the map. We define topological version of uniform rigidity and show that on a compact and T3 space any dynamical system is topologically uniformly rigid if it is first countable, almost topologically equicontinuous and transitive or it is second countable, topologically equicontinuous and has a dense set of periodic points. We show that a topologically uniformly rigid dynamical system, on a compact, Hausdorff space, has zero topological entropy. Moreover, we provide necessary examples and counterexamples.
DOI : 10.2298/FIL2320813K
Classification : 37B40, 37B02, 54A20, 54B10
Keywords: Topological equicontinuity, Topological uniform rigidity, Topological entropy, Transitivity 
Devender Kumar; Ruchi Das. Topological equicontinuity and topological uniform rigidity for dynamical system. Filomat, Tome 37 (2023) no. 20, p. 6813 . doi: 10.2298/FIL2320813K
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     doi = {10.2298/FIL2320813K},
     language = {en},
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