Notes on Hamiltonian Dynamical Systems

"A major role in the development of the theory of classical dynamical systems is played by the Hamiltonian formulation of the equations of dynamics. This chapter is intended to provide a basic knowledge of the formalism, assuming that the Lagrangian formalism is known. A reader already familiar with the canonical formalism may want to skip the present chapter"--

List of contents

1. Hamiltonian formalism; 2. Canonical transformations; 3. Integrable systems; 4. First integrals; 5. Nonlinear oscillations; 6. The method of Lie series and of Lie transform; 7. The normal form of Poincaré and Birkhoff; 8. Persistence of invariant tori; 9. Long time stability; 10. Stability and chaos; A. The geometry of resonances; B. A quick introduction to symplectic geometry; References; Index.

About the author

Antonio Giorgilli is a retired Professor of Mathematics at the Università degli Studi di Milano and has been elected corresponding member of Istituto Lombardo Accademia di Scienze e Lettere since 2005. He has taught courses in mathematical physics and dynamical systems ranging from undergraduate to PhD level. His research in dynamical systems focuses on the characterization of chaos, KAM theory and Nekhoroshev's theory on exponential stability. In addition to being an Invited Speaker of the 1998 International Congress of Mathematicians, Giorgilli's other notable honors include the International Gili Agostinelli Prize for Pure or Applied Mechanics or Classical Mathematical Physics by the Accademia delle Scienze di Torino in 2007. The minor planet 27855 Giorgilli, discovered in 1995, is named in his honor.

Product details

• Authors: Antonio Giorgilli, Antonio (Universita Degli Studi DI Mila Giorgilli, Giorgilli Antonio
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.05.2022
• EAN: 9781009151146
• ISBN: 978-1-0-0915114-6
• No. of pages: 460
• Series: London Mathematical Society Student Texts; London Mathematical Society St
• Subjects: Natural sciences, medicine, IT, technology > Physics, astronomy > Miscellaneous; SCIENCE / Physics / Mathematical & Computational, SCIENCE / Mechanics / Dynamics, Mathematical physics, Dynamics & statics, SCIENCE / Mechanics / Statics, Dynamics and statics, Mathematical / Computational / Theoretical physics