We study various aspects of the dynamics induced by integer matrices on the
invariant rational lattices of the torus in dimension 2 and greater. Firstly,
we investigate the orbit structure when the toral endomorphism is not
invertible on the lattice, characterising the pretails of eventually periodic
orbits. Next we study the nature of the symmetries and reversing symmetries of
toral automorphisms on a given lattice, which has particular relevance to
(quantum) cat maps.Comment: 29 pages, 3 figure

A. Fel'shtyn

A. Katok

D. D. Wall

D. Damanik

D. Ruelle

E. Behrends

E. Brown

F. J. Dyson

F. R. Gantmacher

G. Gaspari

H. Aydin

H. Hasse

H. T. Engstrom

I. Percival

J. A. G. Roberts

J. P. Keating

John A. G. Roberts

M. Baake

M. Degli Esposti

M. Ward

Michael Baake

N. Avni

N. J. A. Sloane

N. Jacobson

N. Neumärker

N. Zierler

Natascha Neumärker

O. Taussky

P. Bundschuh

P. Kurlberg

P. Seibt

P. Walters

R. Adler

R. De Vogelaere

R. J. Wilson

R. Lidl

R. W. Davis

S. Lang

V. I. Arnold

W. A. Adkins

English

arXiv

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Discrete and Continuous Dynamical Systems

Orbit structure and (reversing) symmetries
of toral endomorphisms on rational lattices

Baake M, Neumärker N. Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices. Discrete and continuous dynamical systems A. 2012;33(2):527-553.We study various aspects of the dynamics induced by integer matrices on the invariant rational lattices of the torus in dimension [2] and greater. Firstly, we investigate the orbit structure when the toral endomorphism is not invertible on the lattice, characterising the pretails of eventually periodic orbits. Next we study the nature of the symmetries and reversing symmetries of toral automorphisms on a given lattice, which has particular relevance to (quantum) cat maps

Baake, Michael

Neumärker, Natascha

Publications at Bielefeld University

A generalization of a paper by

A note on the dynamical zeta function of general toral endomorphisms,

A period formula for torus automorphisms,

Algebra { An Approach via Module Theory,&quot; corr. 2nd printing,

Algebra,&quot;

An Introduction to Ergodic Theory,&quot; Graduate Texts in

Arithmetical properties of strongly chaotic motions,

arker, \Orbitstatistik und Relative Realisierbarkeit,&quot; Diploma Thesis,

arker, \The Arithmetic Structure of Discrete Dynamical Systems on the Torus,&quot;

Asymptotic properties of the periodic orbits of the cat maps,

Certain matrix equations over rings of integers,

Chaos and time-reversal symmetry. Order and chaos inreversible dynamical systems,

Cycles of directed graphs de matrix multiplication (mod n),

Distribution of closed orbits for linear automorphisms of tori,

Dynamical Zeta Functions for Piecewise Monotone Maps of the Interval,&quot;

Dynamical zeta functions, nielsen theory and reidemeister torsion, Memoirs AMS,

Ergodic Problems of Classical Mechanics,&quot; reprint, AddisonWesley,

Fibonacci series modulo m,

Gordon-type arguments in the spectral theory of one-dimensional quasicrystals,

Hecke theory and equidistribution for the quantization of linear maps of the torus,

Introduction into connections between algebraic number theory and integral matrices, 2nd appendix to:} . Cohn, A Classical Invitation to Algebraic Numbers and Class Fields, 2nd printing,

Introduction to Finite Fields and Their Applications,&quot;

Introduction to Graph Theory,&quot;

Introduction to the Modern Theory of Dynamical Systems,&quot;

Lectures in Abstract Algebra. II. Linear Algebra,&quot;

Linear recurring sequences,

matrices over a localprincipal ideal ring,

Matrix Theory,&quot;

Number Theory,&quot;

On sequences de by linear recurrence relations,

On the order of unimodular matrices modulo integers,

On the structure of symmetric periodic solutions of conservative systems, with applications,

Period of a discrete cat mapping,

Periodic orbits of linear endomorphisms of the 2-torusand its lattices,

Periods of discretized linear Anosov maps,

Pseudo-symmetries of Anosov maps and spectral statistics,

Reversing symmetry group of GL(2;Z) and PGL(2;Z)matrices with connections to cat maps and trace maps,

symmetries of toral automorphisms,

The arithmetic theory of linear recurring sequences,

The Arnold cat map on prime lattices,

The Online Encyclopedia of Integer Sequences,&quot;

The quantum perturbed cat map and symmetry,

The structure of reversing symmetry groups,

The torus parametrization of quasiperiodic LI-classes,

Topological conjugacy of linear endomorphisms of the 2-torus,

Trace maps as 3D reversible dynamical systems with an invariant,

Trace maps, invariants, and some of their applications,

Wall and Vinston revisited, in \Applications of Fibonacci Numbers,&quot;

Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices

Orbit structure and (reversing) symmetries of toral endomorphisms on
  rational lattices

Orbit structure and (reversing) symmetries of toral endomorphisms on rational lattices

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