On the dimension of points which escape to infinity at given rate under exponential iteration

On the dimension of points which escape to infinity at given rate under exponential iteration

We prove a number of results concerning the Hausdorff and packing dimension of sets of points which escape (at least in average) to infinity at a given rate under non-autonomous iteration of exponential maps. In particular, we generalize the results proved by Sixsmith in 2016 and answer his question...

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Veröffentlicht in:Ergodic theory and dynamical systems 2022-05, Vol.42 (5), p.1591-1623
Hauptverfasser: BARAŃSKI, KRZYSZTOF, KARPIŃSKA, BOGUSŁAWA
Format: Artikel
Sprache:eng
Schlagworte:
Infinity
Mathematics
Original Article
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Beschreibung
Zusammenfassung:We prove a number of results concerning the Hausdorff and packing dimension of sets of points which escape (at least in average) to infinity at a given rate under non-autonomous iteration of exponential maps. In particular, we generalize the results proved by Sixsmith in 2016 and answer his question on annular itineraries for exponential maps.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2021.26