Dynamical complexity and symplectic integrability

Details Dynamical complexity and symplectic integrability Dynamical complexity and symplectic integrability

2009-07-30

arxiv.org/abs/0907.5363v1

Mathematics

Dynamical Systems

58 pages

Scientific paper

We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow entropies", they describe the polynomial growth rate of the number of balls (for the usual "dynamical" distances) of coverings of the ambient space. We then define a new class of integrable systems, which we call decomposable systems, for which one can prove that the weak complexity index is smaller than the number of degrees of freedom. Hamiltonian systems integrable by means of non-degenerate integrals (in Eliasson-Williamson sense), subjected to natural additional assumptions, are the main examples of decomposable systems. We finally give explicit examples of computation of the complexity index, for Morse Hamiltonian systems on surfaces and for two-dimensional gradient systems.

Affiliated with

Also associated with

No associations

Rating

Dynamical complexity and symplectic integrability does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Dynamical complexity and symplectic integrability, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Dynamical complexity and symplectic integrability will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-469197