Take the 2-minute tour ×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.

Consider Arnold's example for Arnold diffusion 1964. $$H=I_1^2/2+I_2^2/2+\epsilon(1-\cos\theta_2)(1+\mu(\sin\theta_1+\sin t)) $$

We can first make it a system of three degrees of freedom.

Then we know this system is not integrable in the Liouville Arnold sense. One integral is the Hamiltonian. Can we find one more integral?

I think the answer should be no. But it is not easy to prove. Maybe one more piece of information is useful. In Arnold's 1964 paper, he calculated two different nonvanishing Melnikov functions.

share|improve this question
    
Maybe the following paper sciencedirect.com/science/article/pii/S0022039603002870 (J. Cresson, Hyperbolicity, transversality and analytic first integrals) will be of some help. –  Zurab Silagadze Apr 11 '13 at 4:41
    
I met a similar problem, but I have no idea what a second integral means. –  user41897 Oct 26 '13 at 17:18
    
integral = integral of the motion = a conserved quantity –  Carlo Beenakker Oct 26 '13 at 20:55
add comment

Know someone who can answer? Share a link to this question via email, Google+, Twitter, or Facebook.

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.