ArticleOriginal scientific text
Title
A version of non-Hamiltonian Liouville equation
Authors 1
Affiliations
- Department of Mathematics and Computer Science, University of Bielsko-Biała, Willowa 2, 43-309 Bielsko-Biała, Poland
Abstract
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
Bibliography
- Spectral Transform and Solitons: Tools to Slove and Investigate Nonlinear Evotion Equations (New York, North-Holland, 1982)
- General solutions to the 2D Liouville equation, Int. J. Engng Sci. 35 (1997) 141-149. doi: 10.1016/S0020-7225(96)00080-8.
- Stochastic Liouville equations, J. Math. Phys. 4 (1963) 174-183. doi: 10.1063/1.1703941.
- Exact solution for the nonlinear Klein-Gordon and Liouville equations in four - dimensional Euklidean space, J. Math. Phys. 28 (1987) 2317-2322. doi: 10.1063/1.527764.
- Mean Value Theorems and Functional Equations (World Scientific Publishing, Singapore, 1998)
- Stationary solutions of Liouville equations for non-Hamiltonian systems, Ann. Phys. 316 (2005) 393-413. doi: 10.1016/j.aop.2004.11.001.
Pages:
5-14
Main language of publication
English
Received
2013-05-08
Published
2014
DOI: 10.7151/dmdico1158
Exact and natural sciences