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TMF, 2015, Volume 183, Number 1, Pages 138–151 (Mi tmf8774)  

Polynomial integrals of motion in dilaton gravity theories

E. A. Davydov

Joint Institute for Nuclear Research, Dubna, Moscow Oblast, Russia

Abstract: Investigating modern gravity and cosmology models involves a stage of analyzing associated nonlinear dynamical systems. In general, such systems are not integrable, but they often admit additional integrals of motion. Based on features of dynamical systems appearing in the theory of dilaton gravity, we formulate a universal algorithm seeking the integrals of motion polynomial in momentum. Using this algorithm, we investigate the dilaton gravity theories with a single scalar field for the presence of linear and quadratic integrals of motion.

Keywords: gravity, dynamical system, integrability, polynomial integral

DOI: https://doi.org/10.4213/tmf8774

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English version:
Theoretical and Mathematical Physics, 2015, 183:1, 567–577

Bibliographic databases:

PACS: 02.30.Ik, 04.50.Kd
MSC: 83D05,83E99, 37J15
Received: 25.06.2014

Citation: E. A. Davydov, “Polynomial integrals of motion in dilaton gravity theories”, TMF, 183:1 (2015), 138–151; Theoret. and Math. Phys., 183:1 (2015), 567–577

Citation in format AMSBIB
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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