Kolmogorov-Arnold-Moser (KAM) Theory

نویسنده

  • Luigi Chierchia
چکیده

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Kam Theory: the Legacy of Kolmogorov’s 1954 Paper

Kolmogorov-Arnold-Moser (or kam) theory was developed for conservative dynamical systems that are nearly integrable. Integrable systems in their phase space usually contain lots of invariant tori, and kam theory establishes persistence results for such tori, which carry quasi-periodic motions. We sketch this theory, which begins with Kolmogorov’s pioneering work.

متن کامل

Quantum analogue of the Kolmogorov–Arnold–Moser transition in field-induced barrier penetration in a quartic potential

Quantum signatures of the Kolmogorov–Arnold– Moser (KAM) transition from the regular to chaotic classical dynamics of a double-well oscillator in the presence of an external monochromatic field of different amplitudes are analysed in terms of the corresponding Bohmian trajectories. It is observed that the classical chaos generally enhances the quantum fluctuations, while the quantum nonclassica...

متن کامل

Quantum KAM Technique and Yang-Mills Quantum Mechanics

We study a quantum analogue of the iterative perturbation theory by Kolmogorov used in the proof of the Kolmogorov-Arnold-Moser (KAM) theorem. The method is based on sequent canonical transformations with a "running" coupling constant ; ; , etc. The proposed scheme, as its classical predecessor, is "superconvergent" in the sense that after the nth step, a theory is solved to the accuracy of ord...

متن کامل

KAM theory in configuration space

A new approach to the Kolmogorov-Arnold-Moser theory concermng the existence of invariant ton having prescnbed frequencies îs presented It îs based on the Lagrangian formahsm m configuration space instead of the Hamiltonian formahsm in phase space used in earher approaches In particular, the construction of the invariant ton avoids the composition of infinitely many coordinate transformations T...

متن کامل

Why Newton's method is hard for travelling waves: Small denominators, KAM theory, Arnold's linear Fourier problem, non-uniqueness, constraints and erratic failure

Nonlinear travelling waves and standing waves can computed by discretizing the appropriate partial differential equations and then solving the resulting system of nonlinear algebraic equations. Here, we show that the “small denominator” problem of Kolmogorov– Arnold–Moser (KAM) theory is equally awkward for numerical algorithms. Furthermore, Newton’s iteration combined with continuation in a pa...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009