5 papers · 1 filter
Self Duality and Codings for Expansive Group Automorphisms
Alex Clark, Robbert Fokkink
Lind and Schmidt have shown that the homoclinic group of a cyclic algebraic dynamical system is isomorphic to the dual of the phase group. We show that this duality result i…
A generalization of Hagopian's theorem and exponents
Alex Clark
We generalize Hagopian's theorem characterizing solenoids to higher dimensions by showing that any homogeneous continuum admitting a fiber bundle projection onto a torus with total…
Exponents and Almost Periodic Orbits
Alex Clark
We introduce the group of exponents of a map of the reals into a metric space and give conditions under which this group embeds in the first Cech cohomology group of the closure of…
Linear Flows on -Solenoids
Alex Clark
Linear flows on inverse limits of tori are defined and it is shown that two linear flows on an inverse limit of tori are equivalent if and only if there is an automorphism of the i…
Flows on solenoids are generically not almost periodic
Alex Clark
The space of non-singular flows on any given solenoid is shown to contain a generic subset consisting of flows that are not almost periodic. Whether this result carries over to Ham…