Banisch, Ralf and Koltai, Péter
(2017)
*Understanding the geometry of transport: diffusion maps for Lagrangian trajectory data unravel coherent sets.*
Chaos: An Interdisciplinary Journal of Nonlinear Science, 23
(23).
ISSN 1054-1500 (print); 1089-7682 (online)
(Submitted)

Full text not available from this repository.

Official URL: http://aip.scitation.org/doi/abs/10.1063/1.4971788

## Abstract

Dynamical systems often exhibit the emergence of long-lived coherent sets, which are regions in state space that keep their geometric integrity to a high extent and thus play an important role in transport. In this article, we provide a method for extracting coherent sets from possibly sparse Lagrangian trajectory data. Our method can be seen as an extension of diffusion maps to trajectory space, and it allows us to construct "dynamical coordinates" which reveal the intrinsic low-dimensional organization of the data. The only a priori knowledge about the dynamics that we require is a locally valid notion of distance, which renders our method highly suitable for automated data analysis. We show convergence of our method to the analytic transfer operator framework of coherence in the infinite data limit, and illustrate its potential on several two- and three-dimensional examples as well as real world data.

Item Type: | Article |
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Subjects: | Mathematical and Computer Sciences |

Divisions: | Department of Mathematics and Computer Science > Institute of Computer Science Department of Mathematics and Computer Science > Institute of Mathematics > BioComputing Group |

ID Code: | 2003 |

Deposited By: | BioComp Admin |

Deposited On: | 09 Jan 2017 13:53 |

Last Modified: | 28 Jun 2017 10:27 |

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