On commuting polynomial automorphisms of Ck{\mathbb{C}}^{k} , k ≥ 3

We characterize the polynomial automorphisms of $C^3,$ which commute with a regular automorphism. We use their meromorphic extension to $P^3$ and consider their dynamics on the hyperplane at infinity. We conjecture the additional hypothesis under which the same characterization is true in all dimensions. We give a partial answer to a question of S. Smale that in our context can be formulated as follows: can any polynomial automorphism of $C^k$ be the uniform limit on compact sets of polynomial automorphisms with trivial centralizer

Long-Term Tracking of Corotating Density Structures Using Heliospheric Imaging

The systematic monitoring of the solar wind in high-cadence and high-resolution heliospheric images taken by the Solar-Terrestrial Relation Observatory (STEREO) spacecraft permits the study of the spatial and temporal evolution of variable solar wind flows from the Sun out to 1 AU, and beyond. As part of the EU Framework 7 (FP7) Heliospheric Cataloguing, Analysis and Techniques Service (HELCATS) project, we have generated a catalog listing the properties of 190 corotating structures well-observed in images taken by the Heliospheric Imager (HI) instruments onboard STEREO-A (ST-A). Based on this catalog, we present here one of very few long-term analyses of solar wind structures advected by the background solar wind. We concentrate on the subset of plasma density structures clearly identified inside corotating structures. This analysis confirms that most of the corotating density structures detected by the heliospheric imagers comprises a series of density inhomogeneities advected by the slow solar wind that eventually become entrained by stream interaction regions. We have derived the spatial-temporal evolution of each of these corotating density structures by using a well-established fitting technique. The mean radial propagation speed of the corotating structures is found to be [Math Processing Error]. Such a low mean value corresponds to the terminal speed of the slow solar wind rather than the speed of stream interfaces, which is typically intermediate between the slow and fast solar wind speeds ([Math Processing Error]). Using our fitting technique, we predicted the arrival time of each corotating density structure at different probes in the inner heliosphere. We find that our derived speeds are systematically lower by [Math Processing Error] than those measured in situ at the predicted impact times. Moreover, for cases when a stream interaction region is clearly detected in situ at the estimated impact time, we find that our derived speeds are lower than the speed of the stream interface measured in situ by an average of [Math Processing Error] at ST-A and [Math Processing Error] at STEREO-B (ST-B). We show that the speeds of the corotating density structures derived using our fitting technique track well the long-term variation of the radial speed of the slow solar wind during solar minimum years (2007 – 2008). Furthermore, we demonstrate that these features originate near the coronal neutral line that eventually becomes the heliospheric current sheet.peerReviewe

The Interaction of Successive Coronal Mass Ejections: A Review

We present a review of the different aspects associated with the interaction of successive coronal mass ejections (CMEs) in the corona and inner heliosphere, focusing on the initiation of series of CMEs, their interaction in the heliosphere, the particle acceleration associated with successive CMEs, and the effect of compound events on Earth’s magnetosphere. The two main mechanisms resulting in the eruption of series of CMEs are sympathetic eruptions, when one eruption triggers another, and homologous eruptions, when a series of similar eruptions originates from one active region. CME – CME interaction may also be associated with two unrelated eruptions. The interaction of successive CMEs has been observed remotely in coronagraphs (with the Large Angle and Spectrometric Coronagraph Experiment – LASCO – since the early 2000s) and heliospheric imagers (since the late 2000s), and inferred from in situ measurements, starting with early measurements in the 1970s. The interaction of two or more CMEs is associated with complex phenomena, including magnetic reconnection, momentum exchange, the propagation of a fast magnetosonic shock through a magnetic ejecta, and changes in the CME expansion. The presence of a preceding CME a few hours before a fast eruption has been found to be connected with higher fluxes of solar energetic particles (SEPs), while CME – CME interaction occurring in the corona is often associated with unusual radio bursts, indicating electron acceleration. Higher suprathermal population, enhanced turbulence and wave activity, stronger shocks, and shock – shock or shock – CME interaction have been proposed as potential physical mechanisms to explain the observed associated SEP events. When measured in situ, CME – CME interaction may be associated with relatively well organized multiple-magnetic cloud events, instances of shocks propagating through a previous magnetic ejecta or more complex ejecta, when the characteristics of the individual eruptions cannot be easily distinguished. CME – CME interaction is associated with some of the most intense recorded geomagnetic storms. The compression of a CME by another and the propagation of a shock inside a magnetic ejecta can lead to extreme values of the southward magnetic field component, sometimes associated with high values of the dynamic pressure. This can result in intense geomagnetic storms, but can also trigger substorms and large earthward motions of the magnetopause, potentially associated with changes in the outer radiation belts. Future in situ measurements in the inner heliosphere by Solar Probe+ and Solar Orbiter may shed light on the evolution of CMEs as they interact, by providing opportunities for conjunction and evolutionary studies