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arXiv · 2204.03527

Geometric aspects of Young Integral: decomposition of flows

Lourival Lima·Paulo Ruffino·Pedro Catuogno
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Abstract

In this paper we study geometric aspects of dynamics generated by Young differential equations (YDE) driven by $\alpha$-H\"older trajectories with $\alpha \in (1/2, 1)$. We present a number of properties and geometrical constructions on this low regularity context: Young It\^o geometrical formula, horizontal lift in principal fibre bundles, parallel transport, covariant derivative, development and anti-development, among others. Our main application here is a geometrical decomposition of flows generated by YDEs according to diffeomorphisms generated by complementary distributions (integrable or not). The proof of existence of this decomposition is based on an Young It\^o-Kunita formula for $\alpha$-H{\"o}lder paths proved by Castrequini and Catuogno (Chaos Solitons Fractals, 2022).

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Lourival Lima, Paulo Ruffino, Pedro Catuogno. 2022-04-07. Geometric aspects of Young Integral: decomposition of flows. https://arxiv.org/abs/2204.03527

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