Uniform stability and chaotic dynamics in nonhomogeneous linear dissipative scalar ordinary differential equations
JOURNAL OF DIFFERENTIAL EQUATIONS(2022)
Abstract
The paper analyzes the structure and the inner long-term dynamics of the invariant compact sets for the skewproduct flow induced by a family of time-dependent ordinary differential equations of nonhomogeneous linear dissipative type. The main assumptions are made on the dissipative term and on the homogeneous linear term of the equations. The rich casuistic includes the uniform stability of the invariant compact sets, as well as the presence of Li-Yorke chaos and Auslander-Yorke chaos inside the attractor.
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Key words
Nonautonomous ordinary differential equations,Dissipativity and global attractor,Chaotic dynamics,Ergodic theory,Lyapunov exponents
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