Natural extensions for p-adic β-shifts and other scaling maps

A new class of $p$-adic Lipschitz functions and multidimensional Hensel's Lemma

“…We think that these constructions are of independent interest and contribute to the study of higher dimensional p-adic analysis, they may as well, stimulate future studies on p-adic dynamics. Some possible directions that may be of interest to the community working on these topics include the study of Bernoulli maps, or more generally of locally scaling functions like in [9,11,15,16]. Another mater that could be of some use is to link the class of p α -Lipschitz functions with the class of compatible functions defined in [4].…”