Item Successfully Added to Cart
An error was encountered while trying to add the item to the cart. Please try again.
OK
Please make all selections above before adding to cart
OK
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems
 
Hasna Riahi Ecole Nationale d’Ingénieurs de Tunis, Tunisia
Front Cover for Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems
Available Formats:
Electronic ISBN: 978-1-4704-0247-1
Product Code: MEMO/138/658.E
112 pp 
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $30.00
Front Cover for Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems
Click above image for expanded view
  • Front Cover for Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems
  • Back Cover for Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems
Study of the Critical Points at Infinity Arising from the Failure of the Palais-Smale Condition for n-Body Type Problems
Hasna Riahi Ecole Nationale d’Ingénieurs de Tunis, Tunisia
Available Formats:
Electronic ISBN:  978-1-4704-0247-1
Product Code:  MEMO/138/658.E
112 pp 
List Price: $50.00
MAA Member Price: $45.00
AMS Member Price: $30.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1381999
    MSC: Primary 58; Secondary 34; 70;

    In this work, the author examines the following: When the Hamiltonian system \(m_i \ddot{q}_i + (\partial V/\partial q_i) (t,q) =0\) with periodicity condition \(q(t+T) = q(t),\; \forall t \in \mathfrak R\) (where \(q_{i} \in \mathfrak R^{\ell}\), \( \ell \ge 3\), \( 1 \le i \le n\), \( q = (q_{1},...,q_{n})\) and \( V = \sum V_{ij}(t,q_{i}-q_{j})\) with \(V_{ij}(t,\xi)\) \(T\)-periodic in \(t\) and singular in \(\xi\) at \(\xi = 0\)) is posed as a variational problem, the corresponding functional does not satisfy the Palais-Smale condition and this leads to the notion of critical points at infinity.

    This volume is a study of these critical points at infinity and of the topology of their stable and unstable manifolds. The potential considered here satisfies the strong force hypothesis which eliminates collision orbits. The details are given for 4-body type problems then generalized to n-body type problems.

    Readership

    Graduate students and research mathematicians working in applications of Morse theory and the study of dynamical systems.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Breakdown of the Palais-Smale condition
    • 3. Morse lemma near infinity
    • 4. A modified functional for the 4-body problem
    • 5. Retraction theorem and related results for the 4-body problem
    • 6. Generalization to the $n$-body problem
  • Request Review Copy
  • Get Permissions
Volume: 1381999
MSC: Primary 58; Secondary 34; 70;

In this work, the author examines the following: When the Hamiltonian system \(m_i \ddot{q}_i + (\partial V/\partial q_i) (t,q) =0\) with periodicity condition \(q(t+T) = q(t),\; \forall t \in \mathfrak R\) (where \(q_{i} \in \mathfrak R^{\ell}\), \( \ell \ge 3\), \( 1 \le i \le n\), \( q = (q_{1},...,q_{n})\) and \( V = \sum V_{ij}(t,q_{i}-q_{j})\) with \(V_{ij}(t,\xi)\) \(T\)-periodic in \(t\) and singular in \(\xi\) at \(\xi = 0\)) is posed as a variational problem, the corresponding functional does not satisfy the Palais-Smale condition and this leads to the notion of critical points at infinity.

This volume is a study of these critical points at infinity and of the topology of their stable and unstable manifolds. The potential considered here satisfies the strong force hypothesis which eliminates collision orbits. The details are given for 4-body type problems then generalized to n-body type problems.

Readership

Graduate students and research mathematicians working in applications of Morse theory and the study of dynamical systems.

  • Chapters
  • 1. Introduction
  • 2. Breakdown of the Palais-Smale condition
  • 3. Morse lemma near infinity
  • 4. A modified functional for the 4-body problem
  • 5. Retraction theorem and related results for the 4-body problem
  • 6. Generalization to the $n$-body problem
Please select which format for which you are requesting permissions.