We study some new types of bifurcation of periodic orbits in the planar three body problem (TBP) consisting of a heavy body (star) and two bodies of small or negligible mass (planets). When one planet has zero mass, we have the restricted TBP. If the massive planet revolves in a circular orbit around the star, we get the circular restricted model (CRTBP) and if its orbit is elliptic, with eccen...

For the family of exponential maps z 7→ exp(z) + κ, we show the following analog of a theorem of Douady and Hubbard concerning polynomials. Suppose that g is a periodic external ray of an exponential map with nonescaping singular value. Then g lands at a repelling or parabolic periodic point. We also show that there are periodic external rays landing at all periodic points of such an exponentia...

There is an open set of right triangles such that for each irrational triangle in this set (i) periodic billiards orbits are dense in the phase space, (ii) there is a unique nonsingular perpendicular billiard orbit which is not periodic, and (iii) the perpendicular periodic orbits fill the corresponding invariant surface.

We show that the blue-sky catastrophe, which creates a stable periodic orbit of unboundedly increasing length, is a typical phenomenon for singularly perturbed (multi-scale) systems with at least two fast variables. Three distinct mechanisms of this bifurcation are described. We argue that it is behind the transition from periodic spiking to periodic bursting oscillations. 2000 Math. Subj. Clas...

There is an open set of right triangles such that for each irrational triangle in this set (i) periodic billiards orbits are dense in the phase space, (ii) there is a unique nonsingular perpendicular billiard orbit which is not periodic, and (iii) the perpendicular periodic orbits fill the corresponding invariant surface.

We demonstrate the utility of the periodic orbit description of chaotic motion by computing from a few periodic orbits highly accurate estimates of a large number of quantum resonances for the classically chaotic 3-disk scattering problem. The symmetry decompositions of the eigenspectra are the same for the classical and the quantum problem, and good agreement between the periodic orbit estimat...

Let f be an orientation preserving homeomorphism of the disc D which possesses a periodic point of period 3. Then either f is isotopic, relative the periodic orbit, to a homeomorphism g which is conjugate to a rotation by 2π/3 or 4π/3, or J has a periodic point of least period n for each n ∈ N∗.

We present polarimetric observations of a massive pre-main sequence short-period binary star of the Herbig Ae/Be type, MWC 1080. The mean polarization at 7660Å is 1.60% at 81.6 • , or 0.6% at 139 • if an estimate of the interstellar polarization is subtracted. The intrinsic polarization points to an asymmetric geometry of the circum-stellar or circumbinary environment while the 139 • intrinsic ...