1,484 research outputs found
On C1-robust transitivity of volume-preserving flows
We prove that a divergence-free and C1-robustly transitive vector field has
no singularities. Moreover, if the vector field is C4 then the linear Poincare
flow associated to it admits a dominated splitting over M
Removing zero Lyapunov exponents in volume-preserving flows
Baraviera and Bonatti proved that it is possible to perturb, in the c^1
topology, a volume-preserving and partial hyperbolic diffeomorphism in order to
obtain a non-zero sum of all the Lyapunov exponents in the central direction.
In this article we obtain the analogous result for volume-preserving flows.Comment: 10 page
Generic dynamics of 4-dimensional C2 Hamiltonian systems
We study the dynamical behaviour of Hamiltonian flows defined on
4-dimensional compact symplectic manifolds. We find the existence of a
C2-residual set of Hamiltonians for which every regular energy surface is
either Anosov or it is in the closure of energy surfaces with zero Lyapunov
exponents a.e. This is in the spirit of the Bochi-Mane dichotomy for
area-preserving diffeomorphisms on compact surfaces and its continuous-time
version for 3-dimensional volume-preserving flows
- …