Titlebook: Symmetries and Semi-invariants in the Analysis of Nonlinear Systems; Laura Menini,Antonio Tornambè Book 2011 Springer-Verlag London Limite

证明无罪

evince

Notation and Background,ential forms. This part is not intended to explain concepts in depth; it indicates how much it is assumed about the background of the reader, and also serves to fix notation. After this review, the Cauchy–Kovalevskaya and the Frobenius theorems are discussed with some details. The last section of th

休息

Analysis of Linear Systems,crete-time linear systems. The idea is that, being simpler to carry out computations in closed form for linear systems, this way the reader can become confident with such concepts before dealing with the unavoidable obstacles brought in by nonlinearities. The chapter is composed of two sections, the

HAUNT

Analysis of Continuous-Time Nonlinear Systems,us-time systems, and their relations with known results in nonlinear systems theory are explored. Such two concepts are strongly related for planar systems, and their relation can be extended to higher order systems through the concept of the inverse Jacobi last multiplier. Before exploring such rel

得意人

Analysis of Discrete-Time Nonlinear Systems,tinuous-time systems, to discrete-time ones. Although there are important obstructions (e.g., it seems not possible to define a concept analogous to the one of orbital symmetry), most of the material is derived without important difficulties, sometimes arriving at a result that is slightly weaker th

DUST

Analysis of Hamiltonian Systems,r–Lagrange systems constituted by the Hamiltonian ones. The Hamiltonian systems are classically defined by using the Poisson brackets, which are strictly connected with first integrals; several properties of the Poisson brackets, as their relation with changes of coordinates, are explored in detail.

dissolution

CRATE

Linearization by State Immersion,ar (and, in general, of higher order) a given nonlinear system. The problem is dealt with both for continuous-time and discrete-time systems. The proposed technique allows, under some assumptions, also the computation of a linearizing diffeomorphism (that does not alter the dimension of the state ve

anticipate

Stability Analysis,results, a detailed study of the scalar case is carried out. Then, for planar systems, first, the connection between the center manifold theory and semi-invariants is pointed out; secondly, the critical cases for which it is possible to derive stability conditions that are easy to check are studied.

lethal

978-1-4471-6241-4Springer-Verlag London Limited 2011