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Stability islands in the vicinity of separatrices of near-integrable symplectic maps

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  • We discuss the problem of existence of elliptic periodic trajectories inside lobes bounded by segments of stable and unstable separatrices of a hyperbolic fixed point. We show that such trajectories generically exist in symplectic maps arbitrary close to integrable ones. Elliptic periodic trajectories as a rule, generate stability islands. The area of such an island is of the same order as the lobe area, but the quotient of areas can be very small. Numerical examples are included.
    Mathematics Subject Classification: Primary: 37J40; Secondary: 70K44, 70H08.

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