Exploring state-space topology in the Geosciences

SCIAMARELLA, DENISSE; CHARÓ, GISELA D.; MICHAEL GHIL; MICKAEL CHECKROUN; ARTANA, GUILLERMO

Paris

Conferencia; The Mathematics of Climate and the Environment (CliMathParis); 2019

Institut Henri Poincaré

Topology plays a central role when it comes to unveiling the underlying structure of chaotic flows from data. The question: 'are there different classes of chaotic behavior?' is intrinsically related with the topology of chaotic attractors in phase space. On the other hand, topology also plays an important role in fluid mechanics, when it comes to a mathematical-physics perspective encompassing applications as diverse as airflow behavior in the larynx up to large-scale dispersion of pollutants in Earth's atmosphere and oceans. This talk provides an overview of scientific progress in both contexts, and examines potential applications of topological methods to the analysis of geophysical flows, with the goal of understanding the basic processes which are most important in describing what we observe, directly or indirectly, in these complex systems.