TY  - THES
AB  - In this thesis, the structure and the distribution of periodic (and preperiodic) orbits in certain discrete dynamical systems on the torus are studied.
The first part is concerned with the action of toral endomorphisms on the rational lattices of the torus.
The connection between fixed point counts on the whole torus and on particular lattices is discussed, and the period lengths on a given lattice are studied in a group-theoretic setting. For non-invertible endomorphisms, the structure of the trees induced on certain lattices, as well as on the union of all rational lattices is investigated.
Furthermore, the symmetry properties of toral endomorphisms
are studied in terms of their (local) symmetry and reversing symmetry groups.
The second part is devoted to the study of               
the Casati-Prosen map for rational parameter pairs,
a two-parameter family of random reversible maps that preserve certain rational lattices of the torus.
Based on exact computations, conjectures concerning the period distribution for certain parameter values are stated and numerical evidence in support of these conjectures is given.
DA  - 2012
KW  - discrete dynamical system
KW  - periodic orbits
KW  - period distribution
KW  - Casati-Prosen map
KW  - trees
KW  - toral endomorphism
LA  - eng
PY  - 2012
TI  - The arithmetic structure of discrete dynamical systems on the torus
UR  - https://nbn-resolving.org/urn:nbn:de:hbz:361-25084753
Y2  - 2024-11-22T04:52:05
ER  -