Open AccessVariants of shadowing properties for iterated function systems on uniform spaces
Author(s) -
Radhika Vasisht,
Mohammad Salman,
Ruchi Das
Publication year - 2021
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2108565v
Subject(s) - mathematics , ergodic theory , iterated function , mixing (physics) , topological space , topology (electrical circuits) , topological dynamics , iterated function system , transitive relation , chain (unit) , function (biology) , pure mathematics , topological tensor product , combinatorics , mathematical analysis , physics , functional analysis , quantum mechanics , astronomy , fractal , evolutionary biology , biology , biochemistry , chemistry , gene
In this paper, the notions of topological shadowing, topological ergodic shadowing, topological chain transitivity and topological chain mixing are introduced and studied for an iterated function system (IFS) on uniform spaces. It is proved that if an IFS has topological shadowing property and is topological chain mixing, then it has topological ergodic shadowing and it is topological mixing. Moreover, if an IFS has topological shadowing property and is topological chain transitive, then it is topologically ergodic and hence topologically transitive. Also, these notions are studied for the product IFS on uniform spaces.