Viability Theory

New Directions

  • Jean-Pierre Aubin
  • Alexandre M. Bayen
  • Patrick Saint-Pierre

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
    Pages 1-40
  3. Viability Kernels and Examples

    1. Front Matter
      Pages 41-41
    2. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 43-104
    3. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 105-124
    4. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 125-177
    5. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 179-197
    6. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 199-245
    7. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 247-270
  4. Mathematical Properties of Viability Kernels

    1. Front Matter
      Pages 271-271
    2. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 273-318
    3. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 319-373
    4. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 375-435
    5. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 437-484
    6. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 485-520
  5. First-Order Partial Differential Equations

    1. Front Matter
      Pages 521-521
    2. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 523-561
    3. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 563-602
    4. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 603-630
    5. Jean-Pierre Aubin, Alexandre M. Bayen, Patrick Saint-Pierre
      Pages 631-680

About this book

Introduction

Viability theory designs and develops mathematical and algorithmic methods for investigating the adaptation to viability constraints of evolutions governed by complex systems under uncertainty that are found in many domains involving living beings, from biological evolution to economics, from environmental sciences to financial markets, from control theory and robotics to cognitive sciences. It involves interdisciplinary investigations spanning fields that have traditionally developed in isolation. The purpose of this book is to present an initiation to applications of viability theory, explaining and motivating the main concepts and  illustrating them with numerous numerical examples taken from various fields.

Keywords

Complex Systems Control Theory Evolutionary Systems Hamilton-Jacobi Equations Viability Theory

Authors and affiliations

  • Jean-Pierre Aubin
    • 1
  • Alexandre M. Bayen
    • 2
  • Patrick Saint-Pierre
    • 3
  1. 1.VIMADESParisFrance
  2. 2.Electrical Engineering and, Computer SciencesUniversity of California at BerkeleyBerkeleyUSA
  3. 3., LEDA-SDFiUniversité Paris DauphineClamartFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-16684-6
  • Copyright Information Springer-Verlag Berlin Heidelberg 2011
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-16683-9
  • Online ISBN 978-3-642-16684-6
  • About this book