ar X iv : m at h / 06 10 64 1 v 1 [ m at h . D S ] 2 1 O ct 2 00 6 Persistence of Hyperbolic Tori in Generalized Hamiltonian Systems ∗

ar X iv : m at h . D S / 06 01 70 1 v 1 28 J an 2 00 6 HYPERBOLICITY VERSUS PARTIAL - HYPERBOLICITY AND THE TRANSVERSALITY - TORSION PHENOMENON

— In this paper, we describe a process to create hyperbolicity in the neighbourhood of a homoclinic orbit to a partially hyperbolic torus for three degrees of freedom Hamiltonian systems: the transversality-torsion phenomenon. keywords: Hyperbolicity, Partially hyperbolic tori, Hamiltonian systems.

ar X iv : m at h - ph / 0 51 00 88 v 1 2 6 O ct 2 00 5 Quasi - Chaplygin Systems and Nonholonimic Rigid Body Dynamics ∗

We show that the Suslov nonholonomic rigid body problem studied in [10, 13, 26] can be regarded almost everywhere as a generalized Chaplygin system. Furthermore, this provides a new example of a multidimensional nonholonomic system which can be reduced to a Hamiltonian form by means of Chaplygin reducing multiplier. Since we deal with Chaplygin systems in the local sense, the invariant manifold...

ar X iv : h ep - l at / 0 11 00 06 v 1 2 O ct 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : h ep - l at / 0 11 00 06 v 2 3 O ct 2 00 1 1 Matrix elements of ∆ S = 2 operators with Wilson fermions

ar X iv : m at h / 06 01 33 8 v 2 [ m at h . D S ] 1 3 A pr 2 00 6 HYPERBOLIC OUTER BILLIARDS : A FIRST EXAMPLE

We present the first example of a hyperbolic outer billiard. More precisely we construct a one parameter family of examples which in some sense correspond to the Bunimovich billiards.