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Next: 6. On the co-existence Up: Rom-Kedar Previous: 4. On the structure

5. Manifolds geometry and transport in 2 dimensional maps

Transport in typical two-dimensional maps is governed by complicated geometrical objects - the stable and unstable manifolds of invariant sets. A careful examination of their structure in the simplest case of a homoclinic tangle reveals that it is possible to find lower bounds on their folding patterns. This approach leads, on one hand, to an approximation scheme for finite time transport (the Topological Approximation Method), and on the other hand to estimates of the Hausdorff dimension of the closure of the unstable manifold.

Collaborators: V. Aframovich.

Michael Grinfeld 2002-10-23