Abstract:Despite many of the most common chaotic dynamical systems being continuous in time, it is through discrete time mappings that much of the understanding of chaos is formed. Henri Poincaré first made this connection by tracking consecutive iterations of the continuous flow with a lower-dimensional, transverse subspace. The mapping that iterates the dynamics through consecutive intersections of the flow with the subspace is now referred to as a Poincaré map, and it is the primary method available for interpreting… Show more
“…Xiao et al (2018) embed sub-samples of datasets with an arbitrary metric into the Euclidean metric to address mode collapse for generative adversarial networks (GANs) (Goodfellow et al, 2014). Bramburger et al (2021) aim to parametrize the Poincaré map by a deep autoencoder architecture that enforces invertibility as a soft constraint.…”
“…Xiao et al (2018) embed sub-samples of datasets with an arbitrary metric into the Euclidean metric to address mode collapse for generative adversarial networks (GANs) (Goodfellow et al, 2014). Bramburger et al (2021) aim to parametrize the Poincaré map by a deep autoencoder architecture that enforces invertibility as a soft constraint.…”
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