Lectures on Twisted Rabinowitz-Floer Homology
Description
This book provides a concise and effective introduction to twisted Rabinowitz-Floer homology, a generalization of Rabinowitz-Floer homology. The theory can be used for finding periodic orbits in Hamiltonian systems: applications include results in celestial mechanics and space mission design.
Written in a style that encourages active reflection and trains problem-solving abilities, the book offers a pathway for aspiring researchers from classical mechanics formulated in the language of symplectic geometry to current research in Rabinowitz-Floer homology and neighboring areas. The book features plenty of examples and exercises, including solutions to most of them, as well as open questions and further directions for research.More details
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Person
Yannis Bähni works in the field of mathematics didactics at ETH Zürich. He holds a PhD in mathematics from the University of Augsburg, Germany.
Content
Chapter 1. Introduction.- Part I. Classical Mechanics.- Chapter 2. The Hamiltonian Formalism.- Chapter 3. The Lagrangian Formalism.- Chapter 4. The Limit Set of a Family of Periodic Orbits.- Part II. Hamiltonian Floer Homology.- Chapter 5. Morse-Bott Homology.- Chapter 6. Bubbling Analysis.- Part III. Twisted Rabinowitz-Floer Homology.- Chapter 7. Definition of Twisted Rabinowitz-Floer Homology.- Chapter 8. Applications of Twisted Rabinowitz-Floer Homology.- Chapter 9. Systolic Geometry.
