V. V. Ivanov, V. M. Cheresiz, “Monotone integrals and stability of autonomous systems”, Sib. Èlektron. Mat. Izv., 2008, Volume 5,Pages <nobr>351

Short communications

Monotone integrals and stability of autonomous systems

V. V. Ivanov, V. M. Cheresiz

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We define the monotone functions of several real variables as well as describe the admissible operations over those and study their geometric structure. The suggested applications of our results to the stability theory of multidimensional dynamical systems are provided.

Keywords: monotone functions of several variables, first integrals and Lyapunov's functions of vector fields, Hamiltonian systems.

UDC: 517.91

MSC: 34C05

Received August 28, 2008, published September 18, 2008