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On eventually always hitting points
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- Ganotaki, Charis (author)
- Lund University,Lunds universitet,Matematik LTH,Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Engineering),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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- Persson, Tomas (author)
- Lund University,Lunds universitet,Dynamiska system,Forskargrupper vid Lunds universitet,Dynamical systems,Lund University Research Groups
- (creator_code:org_t)
- 2021-08-28
- 2021
- English.
- In: Monatshefte fur Mathematik. - : Springer Science and Business Media LLC. - 0026-9255 .- 1436-5081. ; 196:4, s. 763-784
- Journal article (peer-reviewed)
Abstract
Subject headings
Close
- We consider dynamical systems (X, T, μ) which have exponential decay of correlations for either Hölder continuous functions or functions of bounded variation. Given a sequence of balls (Bn)n=1∞, we give sufficient conditions for the set of eventually always hitting points to be of full measure. This is the set of points x such that for all large enough m, there is a k< m with Tk(x) ∈ Bm. We also give an asymptotic estimate as m→ ∞ on the number of k< m with Tk(x) ∈ Bm. As an application, we prove for almost every point x an asymptotic estimate on the number of k≤ m such that ak≥ mt, where t∈ (0 , 1) and ak are the continued fraction coefficients of x.
Subject headings
- NATURVETENSKAP -- Matematik -- Matematisk analys (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Mathematical Analysis (hsv//eng)
Keyword
- Continued fractions
- Eventually always hitting points
- Shrinking targets
Publication and Content Type
- art (subject category)
- ref (subject category)
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