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<center><H2> Dynamical properties of commuting automorphisms </H2></center>

These are expanded notes for a series of lectures
at the
<a href="http://www.math.tugraz.at/DSNT/">Summer School
on Dynamical Systems and Number Theory</a>, Graz
July 9-13, 2007.

<ul>
<li><a href="http://www.mth.uea.ac.uk/~h720/talks/Graz2007/lectures.pdf">Lecture notes</a> (in draft form and subject to change)</li>
<li>Links to original papers available online;
access will depend on your own institution:
<ul>
<li><a href="http://www.jstor.org/view/00029947/di970098/97p0106c/0">
Adler, Konheim &amp; McAndrew (1965):
Topological entropy</li>
<li><a href="http://dx.doi.org/10.1007/BF01746521">
Berg (1969): Convolution of invariant measures, maximal entropy</li>
<li><a href="http://www.jstor.org/view/00029947/di970169/97p00202/0">
Bowen (1971):
Entropy for group endomorphisms and homogeneous spaces</li>
<li><a href="http://dx.doi.org/10.1090/S0002-9947-97-01634-6">
Boyle &amp; Lind (1997): Expansive subdynamics</li>
<li><a href="http://www.mth.uea.ac.uk/~h720/publications/sintdynsys.pdf">
Chothi, Everest &amp; Ward (1997):
<i>S</i>-integer dynamical systems: periodic points</li>
<li><a href="http://dx.doi.org/10.1007/BF00533332">
Conze (1972): Entropie d'un groupe ab&eacute;lien de transformations</li>
<li><a href="http://www.ams.org/journal-getitem?pii=S0002-9947-04-03554-8">
Einsiedler &amp; Lind (2004): Algebraic
<i>Z<sup>d</sup></i>-actions of entropy rank one</li>
<li><a href="http://dx.doi.org/10.1017/S014338570100181X">
Einsiedler, Lind, Miles &amp; Ward (2001):
Expansive subdynamics for algebraic <i>Z<sup>d</sup></i>-actions</li>
<li><a href="http://www.ams.org/journal-getitem?pii=S1079-6762-03-00117-3">
Einsiedler &amp; Lindenstrauss (2003):
Rigidity properties of <i>Z<sup>d</sup></i>-actions on tori and solenoids</li>
<li><a href="http://dx.doi.org/10.1007/PL00000133">
Einsiedler &amp; Rindler (2001):
Algebraic actions of the discrete Heisenberg group and
other non-abelian groups</li>
<li><a href="http://dx.doi.org/10.1017/S0143385702000950">
Einsiedler &amp; Ward (2003):
Asymptotic geometry of non-mixing sequences</li>
<li><a href="http://dx.doi.org/10.1515/crll.2005.2005.584.195">
Einsiedler &amp; Ward (2005):
Entropy geometry and disjointness for zero-dimensional algebraic actions</li>
<li><a href="http://dx.doi.org/10.1007/BF01692494">
Furstenberg (1967):
Disjointness in ergodic theory, minimal sets,
and a problem in diophantine approximation</li>
<li><a href="http://www.jstor.org/view/0003486x/di961645/96p0052p/0">
Haar (1933):
Der Massbegriff in der Theorie der kontinuierlichen Gruppen</a></li>
<li><a href="http://www.jstor.org/view/0003486x/di961654/96p00793/0">
van Kampen (1935):
Locally bicompact abelian groups and their character groups</a></li>
<li><a href="http://dx.doi.org/10.1017/S0143385798110969">
Katok &amp; Spatzier (1998):
Corrections to 'Invariant measures for
higher-rank hyperbolic abelian actions'</li>
<li><a href="http://dx.doi.org/10.2307/1968172">
Lehmer (1933):
Factorization of certain cyclotomic functions</li>
<li><a href="http://dx.doi.org/10.1007/BF01231517">
Lind, Schmidt &amp; Ward (1990):
Mahler measure and entropy for commuting automorphisms of compact groups
</li>
<li><a href="http://www.mth.uea.ac.uk/%7Eh720/publications/padicentropy.pdf">
Lind &amp; Ward (1988):
Automorphisms of solenoids and <i>p</i>-adic entropy</li>
<li><a href="http://dx.doi.org/10.1017/S014338570600054X">
Miles &amp; Ward (2006): Periodic point data detects subdynamics in entropy rank one
</li>
<li><a href="http://dx.doi.org/10.1017/S0143385706000356">
Miles &amp; Ward (2006): Mixing actions of the rationals
</li>
<li><a href="http://www.mth.uea.ac.uk/~h720/talks/Graz2007/nilpotent.pdf">
Miles &amp; Ward (2007):
Orbit-counting for nilpotent group shifts</li>
<li><a href="http://dx.doi.org/10.2307/2006982">
Parry &amp; Pollicott (1983):
An analogue of the prime number theorem for closed orbits of
Axiom A flows</li>
<li><a href="http://dx.doi.org/10.1007/BF01241139">
Rudolph &amp; Schmidt (1995):
Almost block independence and bernoullicity of
<i>Z<sup>d</sup></i>-actions by automorphisms of compact abelian groups</li>
<li><a href="http://dx.doi.org/10.1007/BF01233421">
Schlickewei (1990): <i>S</i>-unit equations over number fields</li>
<li><a href="http://projecteuclid.org/euclid.pjm/1102650389">
Schmidt (1989): Mixing automorphisms of compact groups and a
theorem by Kurt Mahler</li>
<li><a href="http://plms.oxfordjournals.org/cgi/content/abstract/s3-61/3/480">
Schmidt (1990): Automorphisms of compact abelian groups and
affine varieties</li>
<li><a href="http://dx.doi.org/10.1007/BF01231280">
Schmidt &amp; Ward (1993):
Mixing automorphisms of compact groups and a theorem of Schlickewei
</li>
<li><a href="http://dx.doi.org/10.1007/BF01237365">
Sharp (1991): An analogue of Mertens' theorem for closed
orbits of Axiom A flows</li>
<li><a href="http://dx.doi.org/10.1007/BF01297343">
Waddington (1991): 
The prime orbit theorem for quasihyperbolic toral automorphisms</li>
<li><a href="http://nyjm.albany.edu:8000/j/1997/3A_1.html">
Ward (1997): Three Results on Mixing Shapes</li>
<li><a href="http://www.mdpi.org/entropy/papers/e2030142.pdf">
Ward (2000): Additive cellular automata and volume growth</li>
</ul>
</ul>

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