Average-case polynomial-time computability of hamiltonian dynamics

Akitoshi Kawamura, Holger Thies, Martin Ziegler

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We apply average-case complexity theory to physical problems modeled by continuous-time dynamical systems. The computational complexity when simulating such systems for a bounded time-frame mainly stems from trajectories coming close to complex singularities of the system. We show that if for most initial values the trajectories do not come close to singularities the simulation can be done in polynomial time on average. For Hamiltonian systems we relate this to the volume of “almost singularities” in phase space and give some general criteria to show that a Hamiltonian system can be simulated efficiently on average. As an application we show that the planar circular-restricted three-body problem is average-case polynomial-time computable.

Original languageEnglish
Title of host publication43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018
EditorsIgor Potapov, James Worrell, Paul Spirakis
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Print)9783959770866
DOIs
Publication statusPublished - Aug 1 2018
Event43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018 - Liverpool, United Kingdom
Duration: Aug 27 2018Aug 31 2018

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
Volume117
ISSN (Print)1868-8969

Other

Other43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018
CountryUnited Kingdom
CityLiverpool
Period8/27/188/31/18

Fingerprint

Hamiltonians
Trajectories
Polynomials
Computational complexity
Dynamical systems

All Science Journal Classification (ASJC) codes

  • Software

Cite this

Kawamura, A., Thies, H., & Ziegler, M. (2018). Average-case polynomial-time computability of hamiltonian dynamics. In I. Potapov, J. Worrell, & P. Spirakis (Eds.), 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018 [30] (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 117). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.MFCS.2018.30

Average-case polynomial-time computability of hamiltonian dynamics. / Kawamura, Akitoshi; Thies, Holger; Ziegler, Martin.

43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018. ed. / Igor Potapov; James Worrell; Paul Spirakis. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. 30 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 117).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kawamura, A, Thies, H & Ziegler, M 2018, Average-case polynomial-time computability of hamiltonian dynamics. in I Potapov, J Worrell & P Spirakis (eds), 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018., 30, Leibniz International Proceedings in Informatics, LIPIcs, vol. 117, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018, Liverpool, United Kingdom, 8/27/18. https://doi.org/10.4230/LIPIcs.MFCS.2018.30
Kawamura A, Thies H, Ziegler M. Average-case polynomial-time computability of hamiltonian dynamics. In Potapov I, Worrell J, Spirakis P, editors, 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018. 30. (Leibniz International Proceedings in Informatics, LIPIcs). https://doi.org/10.4230/LIPIcs.MFCS.2018.30
Kawamura, Akitoshi ; Thies, Holger ; Ziegler, Martin. / Average-case polynomial-time computability of hamiltonian dynamics. 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018. editor / Igor Potapov ; James Worrell ; Paul Spirakis. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. (Leibniz International Proceedings in Informatics, LIPIcs).
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