14 research outputs found
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
The characteristic exponents of the falling ball model
We study the characteristic exponents of the Hamiltonian system of () point masses freely falling in the vertical half line
under constant gravitation and colliding with each other and
the solid floor elastically. This model was introduced and first studied
by M. Wojtkowski. Hereby we prove his conjecture: All relevant characteristic
(Lyapunov) exponents of the above dynamical system are nonzero, provided that
(i. e. the masses do not increase as we go up) and
Statistical stability and continuity of SRB entropy for systems with Gibbs-Markov structures
We present conditions on families of diffeomorphisms that guarantee
statistical stability and SRB entropy continuity. They rely on the existence of
horseshoe-like sets with infinitely many branches and variable return times. As
an application we consider the family of Henon maps within the set of
Benedicks-Carleson parameters