Simultaneous dense and nondense orbits for noncommuting toral endomorphisms

Simultaneous dense and nondense orbits for noncommuting toral endomorphisms Let S and T be hyperbolic endomorphisms of $${\mathbb {T}}^d$$ T d with the property that the span of the subspace contracted by S along with the subspace contracted by T is $${\mathbb {R}}^d$$ R d . We show that the intersection of the set of points with equidistributing orbit under S with the set of points with nondense orbit under T has maximal Hausdorff dimension. In the case that S and T are quasihyperbolic automorphisms, we prove that the Hausdorff dimension of the intersection is again maximal when we assume that $${\mathbb {R}}^d$$ R d is spanned by the subspaces contracted by S and T along with the central eigenspaces of S and T. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Monatshefte f�r Mathematik Springer Journals

Simultaneous dense and nondense orbits for noncommuting toral endomorphisms

Loading next page...
 
/lp/springer_journal/simultaneous-dense-and-nondense-orbits-for-noncommuting-toral-T10oP9nbMi
Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Austria, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0026-9255
eISSN
1436-5081
D.O.I.
10.1007/s00605-018-1154-2
Publisher site
See Article on Publisher Site

Abstract

Let S and T be hyperbolic endomorphisms of $${\mathbb {T}}^d$$ T d with the property that the span of the subspace contracted by S along with the subspace contracted by T is $${\mathbb {R}}^d$$ R d . We show that the intersection of the set of points with equidistributing orbit under S with the set of points with nondense orbit under T has maximal Hausdorff dimension. In the case that S and T are quasihyperbolic automorphisms, we prove that the Hausdorff dimension of the intersection is again maximal when we assume that $${\mathbb {R}}^d$$ R d is spanned by the subspaces contracted by S and T along with the central eigenspaces of S and T.

Journal

Monatshefte f�r MathematikSpringer Journals

Published: Jan 16, 2018

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off