Salvador Addas-Zanata

Maximizing measures for endomorphisms of the circle

We study a given fixed continuous function and an endomorphism f : S1 → S1, whose f-invariant probability measures maximize . We prove that the set of endomorphisms having a maximizing invariant measure supported on a periodic orbit is dense.

On the stability of some periodic orbits of a new type for twist maps

We study a two-parameter family of twist maps defined on the torus. This family essentially determines the dynamics near saddle-centre loops of four-dimensional real analytic Hamiltonian systems. A saddle-centre loop is an orbit homoclinic to a saddle-centre equilibrium (related to pairs of pure real, ±ν, and pure imaginary, ±ωi, eigenvalues). We prove that given any period n we can find an open set of parameter values such that this family has an attracting n-periodic orbit of a special type. This has interesting consequences on the original Hamiltonian dynamics.

On generic rotationless diffeomorphisms of the annulus

Let f be a C r -diffeomorphism of the closed annulus A that preserves the orientation, the boundary components and the Lebesgue measure. Suppose that f has a lift f to the infinite strip A which has zero Lebesgue measure rotation number. If the rotation number of f restricted to both boundary components of A is positive, then for such a generic f (r > 16), zero is an interior point of its rotation set. This is a partial solution to a conjecture of P. Boyland.

On properties of the vertical rotation interval for twist mappings

In this paper we consider twist mappings of the torus, T : T 2 → T 2 ,a nd their vertical rotation intervals ρV (T ) =( ρ − ,ρ + V ), which are closed intervals such that for any ω ∈) ρ − V ,ρ + V ( there exists a compact T -invariant set Qω with ρV (x) = ω for any x ∈ Qω, where ρV (x) is the vertical rotation number of x. In the case when ω is a rational number, Qω is a periodic orbit. Here we analyze how ρ − and ρ + behave as we perturb T and which dynamical properties for T can be obtained from their values.

Instability for the rotation set of homeomorphisms of the torus homotopic to the identity

In this paper we consider homeomorphisms f : T 2 → T 2 homotopic to the identity and their rotation sets ρ( ˜ f) , which are compact convex subsets of the plane. We show that if ρ( ˜ f) has an extremal point (t, ω) which is not a rational vector, then arbitrarily C 0 close to f we can find a homeomorphism g such that ρ(˜ g) ∩ ρ( ˜ f) c � .

Rational mode locking for homeomorphisms of the 2-torus

Let

On properties of the vertical rotation interval for twist mappings II

f:{\rm T^2\rightarrow T^2}

Homeomorphisms of the annulus with a transitive lift

be a homeomorphism homotopic to the identity,

On maximizing measures of homeomorphisms on compact manifolds

\widetilde{f}:{\rm I}\negthinspace {\rm R^2\rightarrow I} \negthinspace {\rm R^2}

On the existence of a new type of periodic and quasi-periodic orbits for twist maps of the torus

be a fixed lift and