Abstract
We study perturbations of non-recurrent parameters in the exponential family. It is shown that the set of such parameters has Lebesgue measure zero. This particularly implies that the set of escaping parameters has Lebesgue measure zero, which complements a result of Qiu from 1994. Moreover, we show that non-recurrent parameters can be approximated by hyperbolic ones.
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Acknowledgements
We would like to thank Lasse Rempe for useful comments and remarks, and Mats Bylund for some corrections. The second author was partially supported by Vergstiftelsen. We thank the referee for a detailed reading of the manuscript and valuable comments and suggestions.
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Aspenberg, M., Cui, W. Perturbations of exponential maps: Non-recurrent dynamics. JAMA (2024). https://doi.org/10.1007/s11854-024-0340-5
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DOI: https://doi.org/10.1007/s11854-024-0340-5