The subject of local dynamical systems is concerned with the following two questions: 1. Given an n???n matrix A, describe the behavior, in a neighborhood of the origin, of the solutions of all systems of di?erential equations having a rest point at the origin with linear part Ax, that is, all systems of the form x ? = Ax+????????? , n where x? R and the dots denote terms of quadratic and higher order. 2. Describethebehavior(neartheorigin)ofallsystemsclosetoasystem of the type just described. To answer these questions, the ...
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The subject of local dynamical systems is concerned with the following two questions: 1. Given an n???n matrix A, describe the behavior, in a neighborhood of the origin, of the solutions of all systems of di?erential equations having a rest point at the origin with linear part Ax, that is, all systems of the form x ? = Ax+????????? , n where x? R and the dots denote terms of quadratic and higher order. 2. Describethebehavior(neartheorigin)ofallsystemsclosetoasystem of the type just described. To answer these questions, the following steps are employed: 1. A normal form is obtained for the general system with linear part Ax. The normal form is intended to be the simplest form into which any system of the intended type can be transformed by changing the coordinates in a prescribed manner. 2. An unfolding of the normal form is obtained. This is intended to be the simplest form into which all systems close to the original s- tem can be transformed. It will contain parameters, called unfolding parameters, that are not present in the normal form found in step 1. vi Preface 3. The normal form, or its unfolding, is truncated at some degree k, and the behavior of the truncated system is studied.
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Add this copy of Normal Forms and Unfoldings for Local Dynamical Systems to cart. $26.25, very good condition, Sold by Common Crow Books rated 5.0 out of 5 stars, ships from Pittsburgh, PA, UNITED STATES, published 2000 by Springer.
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Add this copy of Normal Forms and Unfoldings for Local Dynamical Systems to cart. $51.65, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2010 by Springer-Verlag New York Inc..
Add this copy of Normal Forms and Unfoldings for Local Dynamical Systems to cart. $51.65, new condition, Sold by Ingram Customer Returns Center rated 5.0 out of 5 stars, ships from NV, USA, published 2002 by Springer.
