• Stephen Wiggins [2003], Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer-Verlag, New York (2nd edition).

• Ferdinand Verhulst [1996], Nonlinear Differential Equations and Dynamical Systems.

• Lawrence Perko [2001], Differential Equations and Dynamical Systems.

• W.S. Koon, M.W. Lo, J.E. Marsden and S.D. Ross [2004], Dynamical Systems, the Three-Body Problem, and Space Mission Design, in preparation.
  • Chapter 2
  • Chapter 6
  • Chapter 7

References on periodic orbits and their computation

• Divakar Viswanath [2001] The Lindstedt-Poincare technique as an algorithm for computing periodic orbits. SIAM Review 43(3), 478-495. (pdf)

• Robert Thurman and Patrick A. Worfolk [1996] The geometry of halo orbits in the circular restricted three-body problem. (pdf)

• K.C. Howell [1984] Three-dimensional, periodic, 'halo' orbits. Celestial Mechanics 32, 53-71. (pdf)

• J.V. Breakwell and J.V. Brown [1979] The 'halo' family of 3-dimensional periodic orbits in the Earth-Moon restricted 3-body problem. Celestial Mechanics 20, 389. (pdf)

References on chaos

• W.S. Koon, M.W. Lo, J.E. Marsden and S.D. Ross [2000], Heteroclinic Connections between Periodic Orbits and Resonance Transitions in Celestial Mechanics, Chaos 10, 427-469. (pdf)

• Stephen Wiggins [1996], An Introduction to the Mechanisms and Methods for the Detection of Chaos, Nonlinear Mathematics and its Applications, in Nonlinear mathematics and its applications (ed. Philip J. Aston). (pdf)

• Philip Holmes [1990] Poincare, celestial mechanics, dynamical-systems theory and "chaos." Physics Reports 193(3), 137-163. (pdf)

• Vered Rom-Kedar and Stephen Wiggins [1990], Transport in Two-Dimensional Maps. Archive for Rational Mechanics and Analysis 109(3), 239-298. (pdf)

References on the Rydberg atom

• C. Jaffe, D. Farrelly, and T. Uzer [1999] Transition state in atomic physics. Physical Review A 60(5), 3833-3850. (pdf)

References on binary asteroids

• Koon, W.S., J.E. Marsden, S.D. Ross, M.W. Lo, and D.J. Scheeres [2003] Geometric mechanics and the dynamics of asteroid pairs. Annals of the New York Academy of Science, to appear. (pdf)

Some additional books just for your information

• J. Guckenheimer and P. Holmes [1983], Nonlinear oscillations, dynamical systems and bifurcations of vector fields, Springer-Verlag, New York.

• A.J. Lichtenberg and M.A. Lieberman [1983], Regular and Stochastic Motion, Springer-Verlag, New York. (find at SFL or purchase at Amazon)

• A.J. Lichtenberg and M.A. Lieberman [1992], Regular and Chaotic Dynamics, Springer-Verlag, New York. (a revised edition of Regular and Stochastic Motion; find at SFL)

• J.M. Ottino [1997], The Kinematics of Mixing: Stretching, Chaos, and Transport, Cambridge University Press, Cambridge (2nd printing).

• Thomas S. Parker and Leon Chua [1989], Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag, New York.

• Stephen Wiggins [1992], Chaotic Transport in Dynamical Systems, Springer-Verlag, New York. (purchase at Amazon)

Research Groups and Departments

• Control and Dynamical Systems, Caltech, USA
  
• Transport and Mixing in Geophysical Flows, Caltech, USA
  
• Barcelona UB-UPC Dynamical Systems Group, Catalunya, Spain
  
• Numerical Mathematics and Dynamical Systems, Univ of Paderborn, Germany
  
• Lab for Advanced Computation in the Math. Sciences, Univ of Bristol, UK
  
• Maryland Chaos Group, Univ of Maryland, USA
  
• Center for Nonlinear Dynamics, Univ of Texas, Austin, USA
  
• Center for Dynamical Systems and Nonlinear Studies, Georgia Tech, USA
  
• Dept of Applied Mathematics, Univ of Colorado at Boulder, USA
  
• Program in Applied and Computational Mathematics, Princeton Univ, USA
  
• Other researchers in dynamical systems and/or astrodynamics
  
  Software for Dynamical Systems Problems
  
• AUTO 2000: a publicly available software package for continuation and bifurcation problems in ordinary differential equations
  
• ODE Software for Matlab: nifty tools like dfield and pplane
  
• Software for maps: by Hinke Osinga
  
  Other References
  
• Matthew Trump's "What is Chaos? A five-part online course for everyone"
  • Dr. Trump is a professor at the Ilya Prigogine Center for Studies in Statistical Mechanics and Complex Systems at the University of Texas at Austin.
• James Meiss's nonlinear science FAQ
  • Dr. Meiss is a professor of Applied Mathematics at the Univ. of Colorado at Boulder.
• Some general references on chaos by the Univ. of Maryland Chaos Group.
  
• Some references on nonlinear dynamics by Carsten Knudsen, University of Leeds, UK.
  

CDS 140b