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Author:   Andre Bellaiche ,  Jean-Jaques Risler
Publisher:   Birkhauser Verlag AG
Imprint:   Birkhauser Verlag AG
Edition:   1996 ed.
Volume:   144
Dimensions:   Width: 15.50cm , Height: 2.30cm , Length: 23.50cm
Weight:   1.660kg
ISBN:  

9783764354763

ISBN 10:   3764354763
Pages:   398
Publication Date:   26 September 1996
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of print, replaced by POD  
We will order this item for you from a manufatured on demand supplier.

Table of Contents

The tangent space in sub-Riemannian geometry.- § 1. Sub-Riemannian manifolds.- § 2. Accessibility.- § 3. Two examples.- § 4. Privileged coordinates.- § 5. The tangent nilpotent Lie algebra and the algebraic structure of the tangent space.- § 6. Gromov’s notion of tangent space.- § 7. Distance estimates and the metric tangent space.- § 8. Why is the tangent space a group?.- References.- Carnot-Carathéodory spaces seen from within.- § 0. Basic definitions, examples and problems.- § 1. Horizontal curves and small C-C balls.- § 2. Hypersurfaces in C-C spaces.- § 3. Carnot-Carathéodory geometry of contact manifolds.- § 4. Pfaffian geometry in the internal light.- § 5. Anisotropic connections.- References.- Survey of singular geodesics.- § 1. Introduction.- § 2. The example and its properties.- § 3. Some open questions.- § 4. Note in proof.- References.- A cornucopia of four-dimensional abnormal sub-Riemannian minimizers.- § 1. Introduction.- § 2. Sub-Riemannian manifolds and abnormal extremals.- § 3. Abnormal extremals in dimension 4.- § 4. Optimality.- § 5. An optimality lemma.- § 6. End of the proof.- § 7. Strict abnormality.- § 8. Conclusion.- References.- Stabilization of controllable systems.- § 0. Introduction.- § 1. Local controllability.- § 2. Sufficient conditions for local stabilizability of locally controllable systems by means of stationary feedback laws.- § 3. Necessary conditions for local stabilizability by means of stationary feedback laws.- § 4. Stabilization by means of time-varying feedback laws.- § 5. Return method and controllability.- References.

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