## From Metastable to Coherent Sets - time-discretization schemes

Please always quote using this URN: urn:nbn:de:0297-zib-66074

- Given a time-dependent stochastic process with trajectories x(t) in a space $\Omega$, there may be sets such that the corresponding trajectories only very rarely cross the boundaries of these sets. We can analyze such a process in terms of metastability or coherence. Metastable sets M are defined in space $M\subset\Omega$, coherent sets $M(t)\subset\Omega$ are defined in space and time. Hence, if we extend the space by the time-variable t, coherent sets are metastable sets in $\Omega\times[0,\infty]$. This relation can be exploited, because there already exist spectral algorithms for the identification of metastable sets. In this article we show that these well-established spectral algorithms (like PCCA+) also identify coherent sets of non-autonomous dynamical systems. For the identification of coherent sets, one has to compute a discretization (a matrix T) of the transfer operator of the process using a space-timediscretization scheme. The article gives an overview about different time-discretization schemes and shows their applicability in two different fields of application.

Author: | Konstantin Fackeldey, Péter Koltai, Peter Névir, Henning Rust, Axel Schild, Marcus Weber |
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Document Type: | ZIB-Report |

Date of first Publication: | 2017/12/08 |

Series (Serial Number): | ZIB-Report (17-74) |

ISSN: | 1438-0064 |