التفاصيل البيبلوغرافية
| العنوان: |
KAM-tori near an analytic elliptic fixed point |
| المؤلفون: |
Eliasson, H., Fayad, B., Krikorian, R. |
| سنة النشر: |
2014 |
| المجموعة: |
Mathematics |
| مصطلحات موضوعية: |
Mathematics - Dynamical Systems |
| الوصف: |
We study the accumulation of an elliptic fixed point of a real analytic Hamiltonian by quasi-periodic invariant tori. We show that a fixed point with Diophantine frequency vector $\o_0$ is always accumulated by invariant complex analytic KAM-tori. Indeed, the following alternative holds: If the Birkhoff normal form of the Hamiltonian at the invariant point satisfies a R\"ussmann transversality condition, the fixed point is accumulated by real analytic KAM-tori which cover positive Lebesgue measure in the phase space (in this part it suffices to assume that $\o_0$ has rationally independent coordinates). If the Birkhoff normal form is degenerate, there exists an analytic subvariety of complex dimension at least $d+1$ passing through 0 that is foliated by complex analytic KAM-tori with frequency $\omega_0$. This is an extension of previous results obtained in \cite{EFK} to the case of an elliptic fixed point. |
| نوع الوثيقة: |
Working Paper |
| URL الوصول: |
http://arxiv.org/abs/1401.5748 |
| رقم الانضمام: |
edsarx.1401.5748 |
| قاعدة البيانات: |
arXiv |