Simultaneously nondense orbits under different expanding maps
(2010) In Dynamical Systems 25(4). p.531545 Abstract
 Given a point and an expanding map on the unit interval, we consider the set of points for which the forward orbit under this map is bounded away from the given point. It is wellknown that in many cases such sets have full Hausdorff dimension. We prove that such sets have a large intersection property, i.e. countable intersections of such sets also have full Hausdorff dimension. This result applies to a class of maps including multiplication by integers modulo 1 and x > 1/x modulo 1. We prove that the same properties hold for multiplication modulo 1 by a dense set of noninteger numbers between 1 and 2.
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1752528
 author
 Färm, David ^{LU}
 organization
 publishing date
 2010
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 noninteger expansions, numbers, badly approximable, Schmidt games, interval maps, Hausdorff dimension
 in
 Dynamical Systems
 volume
 25
 issue
 4
 pages
 531  545
 publisher
 Taylor & Francis
 external identifiers

 wos:000284411900005
 scopus:78649496062
 ISSN
 14689367
 DOI
 10.1080/14689367.2010.482519
 language
 English
 LU publication?
 yes
 id
 a6a3c3b62eda4791b03fc1865be3bad9 (old id 1752528)
 date added to LUP
 20101230 08:39:04
 date last changed
 20180529 11:48:53
@article{a6a3c3b62eda4791b03fc1865be3bad9, abstract = {Given a point and an expanding map on the unit interval, we consider the set of points for which the forward orbit under this map is bounded away from the given point. It is wellknown that in many cases such sets have full Hausdorff dimension. We prove that such sets have a large intersection property, i.e. countable intersections of such sets also have full Hausdorff dimension. This result applies to a class of maps including multiplication by integers modulo 1 and x > 1/x modulo 1. We prove that the same properties hold for multiplication modulo 1 by a dense set of noninteger numbers between 1 and 2.}, author = {Färm, David}, issn = {14689367}, keyword = {noninteger expansions,numbers,badly approximable,Schmidt games,interval maps,Hausdorff dimension}, language = {eng}, number = {4}, pages = {531545}, publisher = {Taylor & Francis}, series = {Dynamical Systems}, title = {Simultaneously nondense orbits under different expanding maps}, url = {http://dx.doi.org/10.1080/14689367.2010.482519}, volume = {25}, year = {2010}, }