Templex : identifying the topological fingerprints of dynamical systems

19 March 2024
Types d’événements
Séminaires du LSCE
Gisele Daniele Charó
Bât. 714, P. 1129
vidéoprojecteur et matériel visio
30 places
19 March 2024
from 11:00 to 12:00

Poincaré described the way in which a dynamical system’s properties depend upon its topology. Topological properties provide detailed information about the fundamental mechanisms — stretching, squeezing, tearing, folding, twisting — that act to shape a dynamical system’s flow in state space. A topological analysis involves finding a topological representation of the underlying structure and obtaining an algebraic description that allows for the computation of topological invariants. The present work proposes fingerprinting a model’s or system’s nonlinear behaviour using the novel concept of templex. The templex has two components: a cell complex and a directed graph. In the deterministic framework, the cell complex approximates the branched manifold, and the directed graph prescribes the allowed connections between the highest-dimensional cells of the complex according to the flow. The templex properties include the non-equivalent ways of circulating along the complex, which are essential to provide a full description of the ‘topological fingerprints’ of the system’s dynamics. [Chaos 2022, doi:10.1063/5.0092933]

LSCE