TY - GEN
T1 - Average-case polynomial-time computability of hamiltonian dynamics
AU - Kawamura, Akitoshi
AU - Thies, Holger
AU - Ziegler, Martin
N1 - Funding Information:
Acknowledgements This work was supported by the Japan Society for the Promotion of Science (JSPS), Core-to-Core Program (A. Advanced Research Networks), JSPS KAKENHI Grant Numbers JP18H03203 and JP18J10407, the Korean Ministry of Science and ICT grant NRF-2016K1A3A7A03950702. We thank Florian Steinberg for discussions on average-case complexity in analysis and the anonymous reviewers for many helpful comments.
Publisher Copyright:
© Akitoshi Kawamura, Holger Thies, and Martin Ziegler.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - 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.
AB - 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.
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U2 - 10.4230/LIPIcs.MFCS.2018.30
DO - 10.4230/LIPIcs.MFCS.2018.30
M3 - Conference contribution
AN - SCOPUS:85053202427
SN - 9783959770866
T3 - Leibniz International Proceedings in Informatics, LIPIcs
BT - 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018
A2 - Potapov, Igor
A2 - Worrell, James
A2 - Spirakis, Paul
PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
T2 - 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018
Y2 - 27 August 2018 through 31 August 2018
ER -