A version of non-Hamiltonian Liouville equation

Celina Rom

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2014)

  • Volume: 34, Issue: 1, page 5-14
  • ISSN: 1509-9407

Abstract

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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.

How to cite

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Celina Rom. "A version of non-Hamiltonian Liouville equation." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 34.1 (2014): 5-14. <http://eudml.org/doc/270735>.

@article{CelinaRom2014,
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.},
author = {Celina Rom},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {Liouville equation; invariant measure},
language = {eng},
number = {1},
pages = {5-14},
title = {A version of non-Hamiltonian Liouville equation},
url = {http://eudml.org/doc/270735},
volume = {34},
year = {2014},
}

TY - JOUR
AU - Celina Rom
TI - A version of non-Hamiltonian Liouville equation
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2014
VL - 34
IS - 1
SP - 5
EP - 14
AB - 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.
LA - eng
KW - Liouville equation; invariant measure
UR - http://eudml.org/doc/270735
ER -

References

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  1. [1] Spectral Transform and Solitons: Tools to Slove and Investigate Nonlinear Evotion Equations (New York, North-Holland, 1982) 
  2. [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. [3] Stochastic Liouville equations, J. Math. Phys. 4 (1963) 174-183. doi: 10.1063/1.1703941. Zbl0135.45102
  4. [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. Zbl0663.35077
  5. [5] Mean Value Theorems and Functional Equations (World Scientific Publishing, Singapore, 1998) 
  6. [6] Stationary solutions of Liouville equations for non-Hamiltonian systems, Ann. Phys. 316 (2005) 393-413. doi: 10.1016/j.aop.2004.11.001. Zbl1073.82503

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