Science and Technology Production
Congress
Authorship
Ghil, Michael
;
CHARÓ, GISELA DANIELA
;
Denisse Sciamarella
;
Pierini, Stefano
Date
2025
Publishing House and Editing Place
American Mathematical Society
Summary
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SIGEVA
The theory of nonautonomous and random dynamical systems (NDSs and RDSs) provides an appropriate mathematical setting for the study of time-dependent forcing, both natural and anthropogenic, upon a climate system characterized by intrinsic variability [1]. In this theory, the forward attractors of autonomous dynamical systems are replaced by pullback and random attractors (PBAs and RAs) and classical bifurcations by “tipping points.” Over the last decade- and-a-half, these relativel...
The theory of nonautonomous and random dynamical systems (NDSs and RDSs) provides an appropriate mathematical setting for the study of time-dependent forcing, both natural and anthropogenic, upon a climate system characterized by intrinsic variability [1]. In this theory, the forward attractors of autonomous dynamical systems are replaced by pullback and random attractors (PBAs and RAs) and classical bifurcations by “tipping points.” Over the last decade- and-a-half, these relatively novel concepts have been applied to a number of simple climate models, atmospheric, oceanic and coupled [2]. Important insights into the study of PBAs and RAs arising from climate dynamics have been provided by novel tools from algebraic topology [3,4]. These tools have led to the introduction and analysis of topological tipping points and we present them here as applied to a simple model of the wind-driven double-gyre ocean circulation [5]. The model is a low-order approximation of a spectral quasigeostrophic model for the sub- tropical and subpolar gyres of the North Atlantic or North Pacific ocean basin, subject to time varying zonal winds [6]. The recent tools from algebraic topology applied to it are Branched Manifold Analysis through Homologies (BraMAH) and the Templex, which combines the com- plex underlying BraMAH with a directed graph that captures the flow in the dynamical system’s phase space [4].
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Key Words
TEMPLEXPULLBACK ATTRACTORSDOUBLE GYRE