A version of non-Hamiltonian Liouville equation

• Autorzy: Celina Rom
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Liouville equation; invariant measure

Kategorie tematyczne

• 34A99: None of the above, but in this section

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2014
• Tom: 34
• Numer: 1
• Strony: 5-14

Daty

wydano

2014

otrzymano

2013-05-08

Twórcy

autor

Celina Rom

• Department of Mathematics and Computer Science, University of Bielsko-Biała, Willowa 2, 43-309 Bielsko-Biała, Poland

Bibliografia

• [1] Spectral Transform and Solitons: Tools to Slove and Investigate Nonlinear Evotion Equations (New York, North-Holland, 1982)
• [2] General solutions to the 2D Liouville equation, Int. J. Engng Sci. 35 (1997) 141-149. doi: 10.1016/S0020-7225(96)00080-8.
• [3] Stochastic Liouville equations, J. Math. Phys. 4 (1963) 174-183. doi: 10.1063/1.1703941.
• [4] 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.
• [5] Mean Value Theorems and Functional Equations (World Scientific Publishing, Singapore, 1998)
• [6] Stationary solutions of Liouville equations for non-Hamiltonian systems, Ann. Phys. 316 (2005) 393-413. doi: 10.1016/j.aop.2004.11.001.

Identyfikatory

DOI

10.7151/dmdico1158