Periodic points and smooth rays

Periodic Orbits , Externals Rays And

Periodic Points

B-spaces are a class of uniquely arcwise connected generalized continua, containing trees. In this paper, it is shown that a main result obtained by several authors for existence of periodic points of small periods of mappings of trees is also true for B-spaces.

Repelling periodic points and landing of rays for post-singularly bounded exponential maps

We show that repelling periodic points are landing points of periodic rays for exponential maps whose singular value has bounded orbit. For polynomials with connected Julia sets, this is a celebrated theorem by Douady, for which we present a new proof. In both cases we also show that points in hyperbolic sets are accessible by at least one and at most finitely many rays. For exponentials this a...

Integer Sequences and Periodic Points

Arithmetic properties of integer sequences counting periodic points are studied, and applied to the case of linear recurrence sequences, Bernoulli numerators, and Bernoulli denominators.

Morphic Heights and Periodic Points

An approach to the calculation of local canonical morphic heights is described, motivated by the analogy between the classical height in Diophantine geometry and entropy in algebraic dynamics. We consider cases where the local morphic height is expressed as an integral average of the logarithmic distance to the closure of the periodic points of the underlying morphism. The results may be though...