The existences of transverse homoclinic solutions and chaos for parabolic equations
DOI10.1016/j.jmaa.2006.11.057zbMath1203.34094OpenAlexW1991022284MaRDI QIDQ2642137
Guangping Luo, Chang Rong Zhu, Yong Lu Shu
Publication date: 20 August 2007
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.11.057
chaotic motionexponential dichotomyLyapunov-Schmidt methodhomoclinic bifurcationshadowing lemmapersistence of homoclinic orbits
Abstract parabolic equations (35K90) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Nonlinear differential equations in abstract spaces (34G20) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Complex behavior and chaotic systems of ordinary differential equations (34C28) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Dichotomy, trichotomy of solutions to ordinary differential equations (34D09)
Related Items (2)
Cites Work
- Exponential dichotomies and homoclinic orbits in functional differential equations
- Heteroclinic orbits for retarded functional differential equations
- Geometric theory of semilinear parabolic equations
- The existence of transverse homoclinic solutions for higher order equations
- Exponential dichotomies and transversal homoclinic points
- Homoclinic solutions for autonomous ordinary differential equations with nonautonomous perturbations
- Transverse homoclinic orbits in periodically perturbed parabolic equations
- Bifurcation from a homoclinic orbit in parabolic differential equations
- Homoclinic Solutions for Autonomous Dynamical Systems in Arbitrary Dimension
- Bounded solutions for non-autonomous parabolic equations
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