This book provides a concise and effective introduction to twisted RabinowitzFloer homology, a generalization of RabinowitzFloer 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 RabinowitzFloer 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.
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. MorseBott Homology.
Chapter
6. Bubbling Analysis.-
Part III. Twisted RabinowitzFloer Homology.
Chapter
7. Definition of
Twisted RabinowitzFloer Homology.
Chapter
8. Applications of Twisted
RabinowitzFloer Homology.
Chapter
9. Systolic Geometry.
Yannis Bähni works in the field of mathematics didactics at ETH Zürich. He holds a PhD in mathematics from the University of Augsburg, Germany.
