Transversality of homoclinic orbits and exponential dichotomies for parabolic equations

DOI10.1006/JMAA.1997.5662zbMath0891.58037OpenAlexW2000709727MaRDI QIDQ1378737

Weiyao Zeng

Publication date: 6 July 1998

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1997.5662

zbMATH Keywords

transversalityhomoclinic orbitsexponential dichotomieslinear parabolic equations

Mathematics Subject Classification ID

Heat and other parabolic equation methods for PDEs on manifolds (58J35) Higher-order parabolic equations (35K25)

Related Items (6)

Exponential dichotomies, the Fredholm alternative, and transverse homoclinic orbits in partial functional differential equations ⋮ New class of perturbations for nonuniform exponential dichotomy roughness ⋮ Robustness of nonuniform exponential dichotomies in Banach spaces ⋮ Fredholm operators and nonuniform exponential dichotomies ⋮ Nonuniform exponential dichotomies and Fredholm operators for flows ⋮ Existence of nonuniform exponential dichotomies and a Fredholm alternative

Cites Work

• Unnamed Item
• Unnamed Item
• An introduction to infinite dimensional dynamical systems -- geometric theory. With an appendix by Krzysztof P. Rybakowski
• Exponential dichotomies and homoclinic orbits in functional differential equations
• Transversal heteroclinic points and Cherry's example of a nonintegrable Hamiltonian system
• An example of bifurcation to homoclinic orbits
• Geometric theory of semilinear parabolic equations
• Global bifurcations and chaos. Analytical methods
• Existence of dichotomies and invariant splittings for linear differential systems. I
• Dichotomies in stability theory
• Heteroclinic orbits in singular systems: A unifying approach
• Dichotomies for linear evolutionary equations in Banach spaces
• Exponential dichotomies and transversal homoclinic points
• The Fredholm alternative and exponential dichotomies for parabolic equation
• Existence and roughness of the exponential dichotomy for skew-product semiflow in Banach spaces
• Asymptotic almost periodicity of scalar parabolic equations with almost periodic time dependence
• Exponential dichotomies and transversal homoclinic orbits in degenerate cases
• Heteroclinic orbits of semilinear parabolic equations
• Melnikov Transforms, Bernoulli Bundles, and Almost Periodic Perturbations
• Transverse homoclinic orbits in periodically perturbed parabolic equations
• On Minimal Sets of Scalar Parabolic Equations with Skew-Product Structures

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