Large part of my research interests used to be centered around the concept of the monodromy matrix in its many forms and names:
- The Fundamental Solution Matrix,
- The Ordered Exponential Matrix,
- The Floquet Matrix.
It is an integral matrix characterization of the periodic dynamical systems. John Baez gives nice layman explanation what it is. Related concepts are the Monodromy Group and the Monodromy Principle.
- Discussion on Monodromy in sci.physics.research newsgroup, by John Baez – http://www.lns.cornell.edu/spr/2002-08/msg0043786.html
- Definition of Monodromy in the Computer Algebra and Algebraic Geometry — Achievements and Perspectives speach by Gert-Martin Greuel – http://www.mathematik.uni-kl.de/~zca/Reports_on_ca/29/paper_html/node12.html
- The Monodromy Principle section in the Complex Analysis slide presentation by Harold V. McIntosh – http://delta.cs.cinvestav.mx/~mcintosh/comun/complex/node30.html
- Monodromy Group at the Mathworld – http://mathworld.wolfram.com/MonodromyGroup.html
- Orbit Stability Analysis Panel: Eigenvalues of the Monodromy Matrix – http://www.geom.uiuc.edu/~megraw/SOFTWARE/ORBIT_PANEL/eig_fields.html – an online calculator
- The Fundamental Solution Matrix and Stability of Halo Orbits – http://www.geom.uiuc.edu/~megraw/CR3BP_html/cr3bp_mono.html