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Computer-Assisted Proofs for Dynamical Systems

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Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations

Part of the book series: Springer Series in Computational Mathematics ((SSCM,volume 53))

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Abstract

In the last two decades, a significant branch of research on dynamical systems with ordinary and partial differential equations has arisen within the global field of computer-assisted proofs and verified numerics. The authors of this book did not actively contribute to this subject, but we believe that some rough description of these approaches should be given here. However, we are not aiming at a complete overview of the results established in the dynamical systems community, but want to comment on what we believe are the main ideas.

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Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, Fukuoka, Japan

    Mitsuhiro T. Nakao

  2. Faculty of Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany

    Michael Plum

  3. Research Institute for Information Technology, Kyushu University, Fukuoka, Japan

    Yoshitaka Watanabe

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  1. Mitsuhiro T. Nakao
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  2. Michael Plum
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  3. Yoshitaka Watanabe
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Nakao, M.T., Plum, M., Watanabe, Y. (2019). Computer-Assisted Proofs for Dynamical Systems. In: Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations. Springer Series in Computational Mathematics, vol 53. Springer, Singapore. https://doi.org/10.1007/978-981-13-7669-6_11

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