Coexistence of periods in a bisecting bifurcation

The inner structure of the attractor appearing when the Varley-Gradwell-Hassell population model bifurcates from regular to chaotic behaviour is studied. By algebraic and geometric arguments the coexistence of a continuum of neutrally stable limit cycles with different periods in the attractor is explained.Comment: 13 pages, 5 figure

Multiband polarimetric and total intensity imaging of 3C345

We monitored the superluminal QSO 3C 345 at three epochs during a one-year period in 1995--1996, observing with the VLBA at 22, 15, 8.4, and 5 GHz. We imaged the radio source both in total and in polarized intensity. In the images at 5 and 8.4 GHz, the jet emission is traced up to 20 milliarcseconds (mas) from the jet core. In the 15 and 22 GHz images, we identify several enhanced emission regions moving at apparent speeds of 5c. Images of the linear polarized emission show predominantly an alignment of the electric vector with the extremely curved jet along the inner part of the high frequency jet. At 5 GHz, the jet shows remarkably strong fractional polarization (m~15%) with the electric vector perpendicular to the jet orientation.Comment: LaTeX file, 6 pages, 2 figures, needs "elsart" style package To be published in New Astronomy Reviews, special issue: Proceedings of the 4th EVN/JIVE VLBI Symposium, Eds. Garrett, M.A., Campbell, R.M., & Gurvits, L.

Families of piecewise linear maps with constant Lyapunov exponent

We consider families of piecewise linear maps in which the moduli of the two slopes take different values. In some parameter regions, despite the variations in the dynamics, the Lyapunov exponent and the topological entropy remain constant. We provide numerical evidence of this fact and we prove it analytically for some special cases. The mechanism is very different from that of the logistic map and we conjecture that the Lyapunov plateaus reflect arithmetic relations between the slopes.Comment: 26 pages, 13 figure

Differential Astrometry over 15 degrees

We observed the pair of radio sources 1150+812 and 1803+784 in November 1993 with a VLBI array, simultaneously recording at 8.4 and 2.3 GHz. We determined the angular separation between the two sources with submilliarcsecond accuracy by using differential techniques. This result demonstrates the feasibility of high precision differential astrometry for radio sources separated in the sky by almost 15 degrees, and opens the avenue to its application to larger samples of radio sources.Comment: 6 pages, latex2e, 2 figures, To appear in the proceedings of the EVN/JIVE Symposium No. 4, New Astronomy Reviews (eds. Garret, M. Campbell, R., and Gurvits, L.

Radio observations of active galactic nuclei with mm-VLBI

Over the past few decades, our knowledge of jets produced by active galactic nuclei (AGN) has greatly progressed thanks to the development of very-long-baseline interferometry (VLBI). Nevertheless, the crucial mechanisms involved in the formation of the plasma flow, as well as those driving its exceptional radiative output up to TeV energies, remain to be clarified. Most likely, these physical processes take place at short separations from the supermassive black hole, on scales which are inaccessible to VLBI observations at centimeter wavelengths. Due to their high synchrotron opacity, the dense and highly magnetized regions in the vicinity of the central engine can only be penetrated when observing at shorter wavelengths, in the millimeter and sub-millimeter regimes. While this was recognized already in the early days of VLBI, it was not until the very recent years that sensitive VLBI imaging at high frequencies has become possible. Ongoing technical development and wide band observing now provide adequate imaging fidelity to carry out more detailed analyses. In this article we overview some open questions concerning the physics of AGN jets, and we discuss the impact of mm-VLBI studies. Among the rich set of results produced so far in this frequency regime, we particularly focus on studies performed at 43 GHz (7 mm) and at 86 GHz (3 mm). Some of the first findings at 230 GHz (1 mm) obtained with the Event Horizon Telescope are also presented.Comment: Published in The Astronomy & Astrophysics Review. Open access: https://link.springer.com/article/10.1007/s00159-017-0105-