GLOSSARY
- Blow-up: a singular (local) transformation allowing one to examine a degenerate singularity of a vector field.
- Center: a singularity of a vector field that is surrounded by an annulus of periodic orbits.
- Center Separatrix: (possibly nonunique) invariant curve, departing in a singular point of a vector field in a direction tangent to an eigendirection of a purely imaginary eigenvalue of the linear part of this vector field. Depending on the direction of the flow on this invariant curve, it is called a stable or an unstable separatrix.
- Center Stable Separatrix:
See Center Separatrix.
- Center Unstable Separatrix:
See Center Separatrix.
- Degenerate Singular Point: a singularity of the vector field where the linear part of the vector field is identically zero.
- Differential System:
See Planar Differential System , Polynomial Differential System.
- Elementary Singular Point: a singularity of the vector field where the linear part has at least one nonzero eigenvalue.
- Elliptic Sector: a region between an unstable and a stable separatrix of a singularity where orbits have the singularity as both their omega-limit and alpha-limit. A region between an unstable and a stable separatrix can also be an hyperbolic sector.
- EPS file: Encapsulated Postscript picture. The picture can be rescaled to any size and can be conveniently included in LaTeX documents.
- FIG file: picture that can be manipulated using the Unix XFIG program (or the Java variant JFIG for Windows/Macintosh).
- Finite Singular Point: a singularity of the vector field in the finite region.
- Focus:
- Focus-center
- Greatest Common Factor
- Hyperbolic Sector
- Hyperbolic Singular Point
- Infinite Singular Point
- Initial Conditions
- Limit Cycles
- Line of Singularities:
- Linear Center
- Node
- Non-degenerate Singular Point
- Non-elementary Singular Point:
- Orbit
- Parabolic Sector
- Parameters controlling the Runge Kutta 7/8 method:
- Parameters controlling the study of the Singular Points:
- Parameters of the Polynomial Differential System:
- Phase Portrait
- Planar Differential System
- Poincare Compactification:
- Poincare Disc
- Poincare-Lyapunov Disc
- Poincare Sphere
- Polynomial Differential System
- Polynomial Vector Field
- REDUCE
- Runge Kutta 7/8
- Saddle
- Saddle-node:
- Sector
- Semi-hyperbolic Singular Point
- Semi-stable Limit Cycle:
See Limit Cycle.
- Separatrix
- Singular Point
- Stable Limit Cycle: See Limit Cycle.
- Stable Node: See Node.
- Stable Separatrix:
See Separatrix.
- Stable Strong Focus:
See Strong Focus
- Stable Weak Focus:
See Weak Focus
- Strong Focus:
- Unstable Limit Cycle:
See Limit Cycle.
- Unstable Node:
See Node.
- Unstable Separatrix:
See Separatrix.
- Unstable Strong Focus:
See Strong Focus
- Unstable Weak Focus:
See Weak Focus
- Weak Focus