Let f : ℂ̂ → ℂ̂ be a subhyperbolic rational map of degree d. We construct a set of "proper" coding maps Cod° (f) = {πr : ∑ → J}r of the Julia set J by geometric coding trees, where the parameter r ranges over mappings from a certain tree to the Ri...

Journal of Physics A: Mathematical and General 37 10571-10584 Nov 2004

Geometrical properties of three-body orbits with zero angular momentum are investigated. If the moment of inertia is also constant along the orbit, the triangle whose vertexes are the positions of the bodies, and the triangle whose perimeters are ...

Journal of the Mathematical Society of Japan 55 439-454 Apr 2003

We define Julia sets for (topological) expanding postcritically finite branched coverings on S2, and show the existence and the uniqueness of Julia sets. Our main aim is the investigation of codings of Julia sets (i.e. semiconjugacies between symb...

Journal of the Mathematical Society of Japan 55 455-468 Apr 2003

We prove that for an expanding postcritically finite branched covering f, the Julia set is orientedly S1-parametrizable if and only if fn is combinatorially equivalent to the degenerate mating of two polynomials for some n > 0.

Acta Mathematica Universitatis Comenianae 71 139-145 Dec 2002

We discuss the relation between (topological) transitivity and strong transitivity of dynamical systems. We show that a transitive and open self-map of a compact metric space satisfying a certain expanding condition is strongly transitive. We also...

Among the ends of this research is to classify branched coverings on the 2-dimensional sphere up to "isotopy." In the 1-dimensional case, we have a good invariant, called a kneading sequence, which divides maps on the interval into "isotopy" class...