Geodesic
A version of non-Hamiltonian Liouville equation
Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 34 (2014) no. 1, pp. 5-14
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In this paper we give a version of the theorem on local integral invariants of systems of ordinary differential equations. We give, as an immediate conclusion of this theorem, a condition which guarantees existence of an invariant measure of local dynamical systems. Results of this type lead to the Liouville equation and have been frequently proved under various assumptions. Our method of the proof is simpler and more direct.
Keywords: Liouville equation, invariant measure 
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Rom, Celina. A version of non-Hamiltonian Liouville equation. Discussiones Mathematicae. Differential Inclusions, Control and Optimization, Tome 34 (2014) no. 1, pp. 5-14. http://geodesic.mathdoc.fr/item/DMDICO_2014_34_1_a0/

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