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Published **2003**
by Springer Berlin Heidelberg in Berlin, Heidelberg .

Written in English

- Geometry,
- Mathematics,
- Global analysis (Mathematics),
- Mechanics

This book contains a mathematical exposition of analogies between classical (Hamiltonian) mechanics, geometrical optics, and hydrodynamics. This theory highlights several general mathematical ideas that appeared in Hamiltonian mechanics, optics and hydrodynamics under different names. In addition, some interesting applications of the general theory of vortices are discussed in the book such as applications in numerical methods, stability theory, and the theory of exact integration of equations of dynamics. The investigation of families of trajectories of Hamiltonian systems can be reduced to problems of multidimensional ideal fluid dynamics. For example, the well-known Hamilton-Jacobi method corresponds to the case of potential flows. The book will be of great interest to researchers and postgraduate students interested in mathematical physics, mechanics, and the theory of differential equations.

**Edition Notes**

Statement | by V. V. Kozlov |

Series | Encyclopaedia of Mathematical Sciences -- 67, Encyclopaedia of Mathematical Sciences -- 67 |

Classifications | |
---|---|

LC Classifications | QA299.6-433 |

The Physical Object | |

Format | [electronic resource] : |

Pagination | 1 online resource (viii, 184 p.) |

Number of Pages | 184 |

ID Numbers | |

Open Library | OL27033438M |

ISBN 10 | 3642075843, 3662068001 |

ISBN 10 | 9783642075841, 9783662068007 |

OCLC/WorldCa | 851379248 |

Dynamical Systems X rd Edition by Victor V. Kozlov (Author) ISBN ISBN Why is ISBN important? ISBN. This bar-code number lets you verify that you're getting exactly the right version or edition of a book. The digit and digit formats both work. Cited by: 8. "Even though there are many dynamical systems books on the market, this book is bound to become a classic. The theory is explained with attractive stories illustrating the theory of dynamical systems, such as the Newton method, the Feigenbaum renormalization picture, fractal geometry, the Perron-Frobenius mechanism, and Google PageRank."/5(9). The English teach mechanics as an experimental science, while on the Continent, it has always been considered a more deductive and a priori science. Unquestionably, the English are right. * H. Poincare, Science and Hypothesis Descartes, Leibnitz, and Newton As is well known, the basic principles of. and Dynamical Systems. Gerald Teschl. This is a preliminary version of the book Ordinary Differential Equations and Dynamical Systems. published by the American Mathematical Society (AMS). This preliminary version is made available with. the permission of the AMS and may not be changed, edited, or reposted at any other website without.

In addition, New ton discussed a large number of problems in mechanics and mathematics in his book, such as the laws of similarity, the theory of impact, special vari ational problems, and algebraicity conditions for Abelian integrals. Almost everything in the Principia subsequently became classic. In this connection, A. N. This chapter focuses on the small noise ergodic dynamical systems. It presents some recent results in small noise problems in the ergodic case and some possible implications for small noise ergodic control problems. It also presents an assumption in which Y 0 (x) is the optimal feedback control in the infinite-time deterministic control problem. Dynamical Systems by Example Barreira, L., Valls, C. () This book comprises an impressive collection of problems that cover a variety of carefully selected topics on the core of the theory of dynamical systems. Linear dynamical systems can be solved in terms of simple functions and the behavior of all orbits classified. In a linear system the phase space is the N-dimensional Euclidean space, so any point in phase space can be represented by a vector with N numbers. The analysis of linear systems is possible because they satisfy a superposition principle: if u(t) and w(t) satisfy the differential.

This is the internet version of Invitation to Dynamical Systems. Unfortunately, the original publisher has let this book go out of print. The version you are now reading is pretty close to the original version (some formatting has changed, so page numbers are unlikely to be the same, and the fonts are diﬀerent). Dynamical Systems is a collection of papers that deals with the generic theory of dynamical systems, in which structural stability becomes associated with a generic property. Some papers describe structural stability in terms of mappings of one manifold into another, as well as their singularities. The book is useful for courses in dynamical systems and chaos, nonlinear dynamics, etc., for advanced undergraduate and postgraduate students in mathematics, physics and engineering. Discover the. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end.

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