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Homoclinical structures in nonautonomous systems: Nonautonomous chaos
L. M. Lerman1, L. P. Shil'nikov
1Research Institute of Applied Mathematics and Cybernetics 10, Ul'yanov st, Nizhny Novgorod, 603005 Russia.
Chaos (Woodbury, N.Y.)
|July 1, 1992
Summary
Researchers introduced integral sets for nonautonomous systems, analogous to homoclinic structures in autonomous systems. Integral curves near these sets are described, advancing the study of dynamical systems.
Area of Science:
- Dynamical Systems Theory
- Nonlinear Dynamics
Background:
- Autonomous systems exhibit complex behaviors like homoclinic structures.
- Understanding nonautonomous systems requires new analytical tools.
Purpose of the Study:
- To introduce and define integral sets for general nonautonomous systems.
- To describe the behavior of integral curves in proximity to these sets.
Main Methods:
- Generalization of concepts from autonomous systems to nonautonomous systems.
- Analysis of integral curves trajectories.
Main Results:
- Definition of integral sets analogous to homoclinic structures.
- Characterization of integral curve behavior near these novel sets.
Conclusions:
- Integral sets provide a framework for understanding complex dynamics in nonautonomous systems.
- The described integral curves offer insights into the structure of these systems.