Seminari del Dipartimento

 

Informatica

Multiple expansions in non-integer bases

Vilmos Komornik


02-02-2022 - 16:00
Largo San Leonardo Murialdo,1 - Pal.C

 

We report on a joint work with Yuru Zou and Jian Lu on multiple expansions in non-integer bases.
Let $U_q^j$ denote the set of real numbers having exactly $j$ expansions in base $q$ over the two-digit alphabet $set{0,1}$.
We investigate the closedness of the sets $U_q^j$.
Next, motivated by an example of Sidorov, we exhibit many special bases in which the Hausdorff dimension of $U_q^j$ is the same for all finite $j$.

Sarà possibile seguire l'evento anche in diretta streaming al seguente link:
https://teams.microsoft.com/dl/launcher/launcher.html?url=%2F_%23%2Fl%2Fmeetup-join%2F19%3A388bb369590943489346c5edc8bb7b83%40thread.tacv2%2F1643444064040%3Fcontext%3D%257b%2522Tid%2522%253a%2522ffb4df68-f464-458c-a546-00fb3af66f6a%2522%252c%2522Oid%2522%253a%252211647586-a255-4c31-b3ea-1a3032a3b0a8%2522%257d%26anon%3Dtrue&type=meetup-join&deeplinkId=226a0064-71d1-4058-acfe-f97c495d2a48&directDl=true&msLaunch=true&enableMobilePage=true&suppressPrompt=true
org: PEDICINI Marco

Copyright© 2014 Dipartimento di Matematica e Fisica