Flow techniques for non-geometric RDEs on manifolds

Hannes Kern; Terry Lyons

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arXiv · 2310.13556

Flow techniques for non-geometric RDEs on manifolds

Hannes Kern·Terry Lyons

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Abstract

In 2015, Bailleul presented a mechanism to solve rough differential equations by constructing flows, using the log-ODE method. We extend this notion in two ways: On the one hand, we localize Bailleul's notion of an almost-flow to solve RDEs on manifolds. On the other hand, we extend his results to non-geometric rough paths, living in any connected, cocommutative, graded Hopf algebra. This requires a new concept, which we call a pseudo bialgebra map. We further connect our results to Curry et al (2020), who solved planarly branched RDEs on homogeneous spaces.

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Hannes Kern, Terry Lyons. 2023-10-20. Flow techniques for non-geometric RDEs on manifolds. https://arxiv.org/abs/2310.13556

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