Hyperbolic properties of four-dimensional symplectic mappings with a structurally unstable trajectory homoclinic to a fixed point of the saddle-focus type
DOI10.1007/BF02757361zbMath0996.37029OpenAlexW1980521572MaRDI QIDQ5951231
L. P. Shil'nikov, Sergey V. Gonchenko
Publication date: 8 August 2002
Published in: Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf02757361
invariant manifoldssymbolic dynamicshomoclinic trajectoryfixed point of saddle-focus typehyperbolic subsetsymplectic diffeomorphism
Symbolic dynamics (37B10) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Stability problems for finite-dimensional Hamiltonian and Lagrangian systems (37J25)
Cites Work
- Invariants of \(\Omega\)-conjugacy of diffeomorphisms with a nongeneric homoclinic trajectory
- Elliptic periodic orbits near a homoclinic tangency in four-dimensional symplectic maps and Hamiltonian systems with three degrees of freedom
- Dynamical phenomena in systems with structurally unstable Poincaré homoclinic orbits
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