Seminar
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| Location: | SLMath: Baker Board Room |
We measure the splitting of invariant manifolds of whiskered(hyperbolic)
tori with three frequencies in a nearly integrable Hamiltonian system,
whose hyperbolic part is given by a pendulum. This splitting depends
strongly on the arithmetic properties of the frequencies. For
3-dimensional frequency vectors, the standard theory of continued
fractions cannot be applied, so we develop a methodology for determining
the behavior of the small divisors for cubic frequencies. A paradigmatic
case is the cubic golden vector, generated by the (real) number
$\Omega=1-\Omega^3$. We show that the splitting is exponential small in
the perturbation parameter $\epsilon$ with an exponent which is a
quasiperiodic function of $\ln\epsilon$. This is a joint work with
Marina Gonchenko and Pere Gutierrez.