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.
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