Opening up fractal structures of three-dimensional flows via leaking

¹ Institut Mediterrani d'Estudis Avançats, CSIC-UIB E-07071 Palma de Mallorca, Spain
² Institut für Physik, Universität Potsdam PF 601553, 14415 Potsdam, Germany
³ Institute for Theoretical Physics, Eötvös University Pf. 32, H-1538, Budapest, Hungary

Received: 8 September 2003
Accepted: 5 January 2004

Abstract

We study the behavior of time-periodic three-dimensional incompressible flows modelled by three-dimensional volume-preserving maps in the presence of a leakage. The distribution of residence times, and the chaotic saddle together with its stable and unstable invariant manifolds are described and characterized. They shed light on typical filamentation of chaotic flows whose local stable and unstable manifolds are always of different character (plane or line). We point out that leaking is a useful method which sheds light on typical filamentation of chaotic flows. In particular, the topology depends on the number of local expanding directions, and is the same in the leaked system as in the closed flow.