Author | Godbillon, Claude. author |
---|---|
Title | Dynamical Systems on Surfaces [electronic resource] / by Claude Godbillon |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1983 |
Connect to | http://dx.doi.org/10.1007/978-3-642-68626-9 |
Descript | VIII, 204 p. online resource |
I. Vector Fields on Manifolds -- 1. Integration of vector fields -- 2. General theory of orbits -- 3. Invariant and minimal sets -- 4. Limit sets -- 5. Direction fields -- A. Vector fields and isotopies -- II. The Local Behaviour of Vector Fields -- 1. Stability and conjugation -- 2. Linear differential equations -- 3. Linear differential equations with constant coefficients -- 4. Linear differential equations with periodic coefficients -- 5. Variation field of a vector field -- 6. Behaviour near a singular point -- 7. Behaviour near a periodic orbit -- A. Conjugation of contractions in R -- III. Planar Vector Fields -- 1. Limit sets in the plane -- 2. Periodic orbits -- 3. Singular points -- 4. The Poincarรฉ index -- 5. Planar direction fields -- 6. Direction, fields on cylinders and Moebius strips -- A. Singular generic foliations of a disc -- IV. Direction Fields on the Torus and Homeomorphisms of the Circle -- 1. Direction fields on the torus -- 2. Direction fields on a Klein bottle -- 3. Homeomorphisms of the circle without periodic point -- 4. Rotation number of Poincarรฉ -- 5. Conjugation of circle homeomorphisms to rotations -- A. Homeomorphism groups of an interval -- B. Homeomorphism groups of the circle -- V. Vector Fields on Surfaces -- 1. Classification of compact surfaces -- 2. Vector fields on surfaces -- 3. The index theorem -- A. Elements of differential geometry of surfaces