عنوان

Sub-Riemannian Geometry

شابک

9783034892100

شابک

9783034899468

شماره

b406317

عنوان اصلي

Sub-Riemannian Geometry

نام عام مواد

[Book]

نام نخستين پديدآور

edited by André Bellaïche, Jean-Jacques Risler.

محل نشرو پخش و غیره

Basel :

نام ناشر، پخش کننده و غيره

Birkhäuser Basel,

تاریخ نشرو بخش و غیره

1996.

عنوان فروست

Progress in Mathematics ;

مشخصه جلد

144

متن يادداشت

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

بدون عنوان

0

متن يادداشت

Sub-Riemannian geometry (also known as Carnot geometry in France, and non-holonomic Riemannian geometry in Russia) has been a full research domain for fifteen years, with motivations and ramifications in several parts of pure and applied mathematics, namely: - control theory - classical mechanics - Riemannian geometry (of which sub-Riemannian geometry constitutes a natural generalization, and where sub-Riemannian metrics may appear as limit cases) - diffusion on manifolds - analysis of hypoelliptic operators - Cauchy-Riemann (or CR) geometry. Although links between these domains had been foreseen by many authors in the past, it is only in recent years that sub- Riemannian geometry has been recognized as a possible common framework for all these topics. This book provides an introduction to sub-Riemannian geometry and presents the state of the art and open problems in the field. It consists of five coherent and original articles by the leading specialists: - André Bellaïche: The tangent space in sub-Riemannian geometry - Mikhael Gromov: Carnot-Carathéodory spaces seen from within - Richard Montgomery: Survey of singular geodesics - Héctor J. Sussmann: A cornucopia of four-dimensional abnormal sub-Riemannian minimizers - Jean-Michel Coron: Stabilization of controllable systems

شماره استاندارد بين المللي کتاب و موسيقي

9783034899468

عنوان

Springer eBooks

موضوع مستند نشده

Global analysis.

موضوع مستند نشده

Global differential geometry.

موضوع مستند نشده

Mathematics.

مستند نام اشخاص تاييد نشده

Bellaïche, André.

مستند نام اشخاص تاييد نشده

Risler, Jean-Jacques.

مستند نام تنالگان تاييد نشده

SpringerLink (Online service)

تاريخ عمليات

20190307162400.0

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y