On closed currents invariant by holomorphic foliations, I

We consider closed positive currents invariant by a singular holomorphic foliation on an algebraic surface. We show that under some conditions the foliation must leave invariant an algebraic curve

Natural Selection: A Stethoscopic Amphibious Installation.

This paper discusses emergence as a complex behaviour in the sound domain and presents a design strategy that was used in the creation of the sound installation Natural Selection to encourage the perception of sonic emergence. The interactions in Natural Selection are based on an algorithm derived from an innately sonic emergent ecological system found in nature, that of mating choices by female frogs within a calling male frog chorus. This paper outlines the design and implementation of the installation and describes the research behind its design, most notably the notion of embodiment within a sonic environment and its importance to the perception of sonic emergence

Discrete orbits, recurrence and solvable subgroups of Diff(C^2,0)

We discuss the local dynamics of a subgroup of Diff(C^2,0) possessing locally discrete orbits as well as the structure of the recurrent set for more general groups. It is proved, in particular, that a subgroup of Diff(C^2,0) possessing locally discrete orbits must be virtually solvable. These results are of considerable interest in problems concerning integrable systems.Comment: The first version of this paper and "A note on integrability and finite orbits for subgroups of Diff(C^n,0)" are an expanded version of our paper "Discrete orbits and special subgroups of Diff(C^n,0)". An intermediate version re-submitted to the journal on March 2015 is available at http://www.fep.up.pt/docentes/hreis/publications.htm where there is also a comparison between these 3 version