Tuesday, June 2, 2020 - 14:15 in ZOOM - Video Conference
On areas of attraction and repulsion in finite time dynamical systems and their numerical approximation
A talk in the Oberseminar Numerik series by
Thorsten Hüls
| Abstract: |
ID 92653100938, Password 1928
Stable and unstable fiber bundles with respect to a fixed
point or a
bounded trajectory are of great dynamical relevance in
(non)autonomous dynamical systems. These sets are defined
via an
infinite limit process. However, the dynamics of several
real world
models are of interest on a short time interval only.
This task requires finite time concepts of attraction and
repulsion
that have been recently developed in the literature.
The main idea consists in replacing the infinite limit
process by a monotonicity criterion and in demanding
the end points to lie in a small neighborhood
of the reference trajectory.
Finite time areas of attraction and repulsion defined in
this way
are fat sets and their dimension equals the dimension of the state
space. We propose an algorithm for the numerical
approximation of
these sets and illustrate its application to several two- and
three-dimensional dynamical systems in discrete and
continuous time.
Intersections of areas of attraction and repulsion are
also calculated,
resulting in finite time homoclinic orbits.
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