http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
MANIFOLDSIntroductionReview of topological conceptsSmooth manifoldsSmooth mapsTangent vectors and the tangent bundleTangent vectors as derivationsThe derivative of a smooth mapOrientationImmersions, embeddings and submersionsRegular and critical points and valuesManifolds with boundarySard's theoremTransversalityStabilityExercisesVECTOR FIELDS AND DYNAMICAL SYSTEMSIntroductionVector fieldsSmooth dynamical systemsLie derivative, Lie bracketDiscrete dynamical systemsHyperbolic fixed points and periodic orbitsExercisesRIEMANNIAN METRICSIntroductionRiemannian metricsStandard geometries on surfaces.
Front cover; Preface; Contents; Chapter 1. Manifolds; Chapter 2. Vector Fields and Dynamical Systems; Chapter 3. Riemannian Metrics; Chapter 4. Riemannian Connections and Geodesics; Chapter 5. Curvature; Chapter 6. Tensors and Differential Forms; Chapter 7. Fixed Points and Intersection Numbers; Chapter 8. Morse Theory; Chapter 9. Hyperbolic Systems; References; Index; Back cover.
Includes bibliographical references and index.
Differential Geometry and Topology : With a View to Dynamical Systems