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Notes on a study of vector bundle dynamical systems (II)—Part 1

✍ Scribed by Liao Shantao

Publisher
Springer
Year
1996
Tongue
English
Weight
674 KB
Volume
17
Category
Article
ISSN
0253-4827

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✦ Synopsis

The study of linear and global propertws of hnear dynamical O:stems on vectol bundles appeared rather extensn'e ah'eady in the past. Presently we propose to study perturbations of this linear dynamics. The perturbed dynamical system whwh we shall consider is no longer linear, while the properties to be studied will be still global in general. Moreover, we are interested m the nonun(formh' hyperbolic properties. In this p.aper, n e set on appropriate definition for such perturbations. Though it appears somewhat not quite usual, yet has deeper root in standard systems of dfferenrial equations m the theory of differentioble dynamical systems. The general problem is to see whwh 1)roper O" of the orig#Tal gzven bv the dynamical O'stem is persistent when a perturbatwn takes place. The whole content of the paper is devoted to establishing a theorem of thzs sort.

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## Comments on: Dynamics and control of a towed underwater vehicle system, part 1: model development The writers wish to congratulate the authors for their outstanding contribution and extremely useful results (Buckam et al., 2003). On the other hand no account is taken for the reduction of cross