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- DYNAMICAL SYSTEMS
- Definition and Related Notation
- Examples of Dynamical Systems
- ELEMENTARY CONCEPTS
- Invariant Sets and Trajectories
- Critical Points and Periodic Points
- Trajectory Closures and Limit Sets
- The First Prolongation and the Prolongational Limit Set
- RECURSIVE CONCEPTS
- Definition of Recursiveness
- Poisson Stable and Non-wandering Points
- Minimal Sets and Recurrent Points
- Lagrange Stability and Existence of Minimal Sets
- DISPERSIVE CONCEPTS
- Unstable and Dispersive Dynamical Systems
- Parallelizable Dynamical Systems
- STABILITY THEORY
- Stability and Attraction for Compact Sets
- Liapunov Functions: Characterization of Asymptotic Stability
- Topological Properties of Regions of Attraction
- Stability and Asymptotic Stability of Closed Sets
- Relative Stability Properties
- Stability of a Motion and Almost Periodic Motions
- FLOW NEAR A COMPACT INVARIANT SET
- Description of Flow near a Compact Invariant Set
- Flow near a Compact Invariant Set (Continued)
- HIGHER PROLONGATIONS
- Definition of Higher Prolongations
- Absolute Stability
- Generalized Recurrence
- C1 - LIAPUNOV FUNCTIONS FOR ORDINARY DIFFERENTIAL EQUATIONS
- Introduction
- Preliminary Definitions and Properties
- Local Theorems
- Extension Theorems
- The Structure of Liapunov Functions
- Theorems Requiring Semidefinite Derivatives
- On the Use of Higher Derivatives of a Liapunov Function
- NON-CONTINUOUS LIAPUNOV FUNCTIONS FOR ORDINARY DIFFERENTIAL EQUATIONS
- Introduction
- A Characterization of Weak Attractors
- Piecewise Differentiable Liapunov Functions
- Local Results
- Extension Theorems
- Non-continuous Liapunov Functions on the Region of Weak Attraction