By Victor A. Sadovnichiy, Mikhail Z. Zgurovsky
Focused on fresh advances, this publication covers theoretical foundations in addition to numerous purposes. It offers sleek mathematical modeling ways to the qualitative and numerical research of options for advanced engineering difficulties in physics, mechanics, biochemistry, geophysics, biology and climatology. Contributions via a world staff of revered authors bridge the space among summary mathematical methods, corresponding to utilized equipment of recent research, algebra, primary and computational mechanics, nonautonomous and stochastic dynamical platforms at the one hand, and useful functions in nonlinear mechanics, optimization, choice making thought and regulate conception at the different. As such, the e-book could be of curiosity to mathematicians and engineers operating on the interface of those fields.
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Extra info for Advances in Dynamical Systems and Control
E. Orel, S. Takahashi ). As a result, a complete classification of the main integrable cases in rigid body dynamics has been obtained up to Liouville equivalence. P. Morozov proved the Liouville equivalence of the Clebsch case  and the Sokolov case  for certain values of the integrals. In , the Liouville equivalence invariants for the Kovalevskaya–Yehia case (this is a generalization of the classical Kovalevskaya top to the case of the problem on the motion of a heavy gyrostat) were calculated.
Their gradients are linearly independent on M almost everywhere. , the natural parameter on their integral trajectories is defined on the whole real axis. 6 The decomposition of the manifold M 2n into connected components of common level surfaces of the integrals f1 , . . , fn is called the Liouville foliation corresponding to the integrable system v = sgrad H. Since f1 , . . , fn are preserved by the flow v, every leaf of the Liouville foliation is an invariant surface. The Liouville foliation consists of regular leaves (filling M almost in the whole) and singular ones (filling a set of zero measure).
American Mathematical Society, Providence (2002) 3. : Uniform trajectory attractor for nonautonomous reaction-diffusion equations with Caratheodory’s nonlinearity. Nonlinear Anal. Theory Methods Appl. 98, 13–26 (2014). 004 4. : Uniform trajectory attractors for nonautonomous dissipative dynamical systems. Continuous and Distributed Systems II. Studies in Systems, Decision and Control Volume 30, pp. 221–232. Springer, New York (2015) 5. : Evolution inclusions and variation Inequalities for Earth data processing III.