Progress in Mathematical Physics

Geography of Order and Chaos in Mechanics

Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools

Authors: Cordani, Bruno

  • Offers a unique approach to the dynamics of quasi-integrable Hamiltonian systems
  • Provides a rare opportunity for readers to experiment with and fully conceptualize recent numerical tools via customized MATLAB applications
  • Gives a rigorous but clean and uncluttered presentation of perturbaton theory, including clear proofs of the KAM and Nekhoroshev theorems
  • Fully describes new, sophisticated techniques for reducing two paradigmatic problems the field to normal forms​
see more benefits

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-0-8176-8370-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-0-8176-8369-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-1-4939-0044-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this book

This original monograph aims to explore the dynamics in the particular but very important and significant case of quasi-integrable Hamiltonian systems, or integrable systems slightly perturbed by other forces. With both analytic and numerical methods, the book studies several of these systems—including for example the hydrogen atom or the solar system, with the associated Arnold web—through modern tools such as the frequency modified fourier transform, wavelets, and the frequency modulation indicator. Meanwhile, it draws heavily on the more standard KAM and Nekhoroshev theorems.

Geography of Order and Chaos in Mechanics will be a valuable resource for professional researchers and certain advanced undergraduate students in mathematics and physics, but mostly will be an exceptional reference for Ph.D. students with an interest in perturbation theory.

Table of contents (10 chapters)

  • Introductory Survey

    Cordani, Bruno

    Pages 1-16

  • Analytical Mechanics and Integrable Systems

    Cordani, Bruno

    Pages 17-81

  • Perturbation Theory

    Cordani, Bruno

    Pages 83-130

  • Numerical Tools I: ODE Integration

    Cordani, Bruno

    Pages 131-146

  • Numerical Tools II: Detecting Order, Chaos, and Resonances

    Cordani, Bruno

    Pages 147-173

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-0-8176-8370-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-0-8176-8369-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.00
price for USA
  • ISBN 978-1-4939-0044-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
Loading...

Recommended for you

Loading...

Bibliographic Information

Bibliographic Information
Book Title
Geography of Order and Chaos in Mechanics
Book Subtitle
Investigations of Quasi-Integrable Systems with Analytical, Numerical, and Graphical Tools
Authors
Series Title
Progress in Mathematical Physics
Series Volume
64
Copyright
2013
Publisher
Birkhäuser Basel
Copyright Holder
Springer Science+Business Media, New York
eBook ISBN
978-0-8176-8370-2
DOI
10.1007/978-0-8176-8370-2
Hardcover ISBN
978-0-8176-8369-6
Softcover ISBN
978-1-4939-0044-2
Series ISSN
1544-9998
Edition Number
1
Number of Pages
XVIII, 334
Topics