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This article is cited in 1 scientific paper (total in 1 paper)
Mathematical problems of nonlinearity
On Almost Shadowable Measures
K. Leea, A. Rojasb a Department of Mathematics, Chungnam National University,
Daejeon 305-764, Republic of Korea
b Instituto de Matemática, Universidade Federal do Rio de Janeiro,
P.O. Box 68530 21945-970, Rio de Janeiro, Brazil
Abstract:
In this paper we study the almost shadowable measures for homeomorphisms on compact
metric spaces. First, we give examples of measures that are not shadowable. Next, we show
that almost shadowable measures are weakly shadowable, namely, that there are Borelians with
a measure close to 1 such that every pseudo-orbit through it can be shadowed. Afterwards, the
set of weakly shadowable measures is shown to be an $F_{\sigma \delta}$ subset of the space of Borel probability
measures. Also, we show that the weakly shadowable measures can be weakly* approximated
by shadowable ones. Furthermore, the closure of the set of shadowable points has full measure
with respect to any weakly shadowable measure. We show that the notions of shadowableness,
almost shadowableness and weak shadowableness coincide for finitely supported measures, or,
for every measure when the set of shadowable points is closed. We investigate the stability of
weakly shadowable expansive measures for homeomorphisms on compact metric spaces.
Keywords:
Shadowable measures, Shadowable points, Homeomorphism.
Received: 25.03.2022 Accepted: 24.04.2022
Citation:
K. Lee, A. Rojas, “On Almost Shadowable Measures”, Rus. J. Nonlin. Dyn., 18:2 (2022), 297–307
Linking options:
https://www.mathnet.ru/eng/nd794 https://www.mathnet.ru/eng/nd/v18/i2/p297
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Abstract page: | 75 | Full-text PDF : | 66 | References: | 16 |
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