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## "Escargot Effect" and the Chandler Wobble Excitation

We study the Chandler wobble (CW) of the pole from 1846 to 2017 extracted by the Panteleev ltering. The CW has period of 433 days, average amplitude of 0.13 milliarcseconds (mas) which is changing, and phase jump by pi in 1930-th. The CW amplitude strongly (almost to zero) decreases in 1930-th and 2010-th with the phase jump in 1930th. The envelope model contains 83- and 42-years quasi-periodicities. We think the rst one can be represented by the 166-years changes of the envelope, crossing zero in 1930th. We reconstruct Chandler input excitation based on the Euler-Liouville equation. Its amplitude has 20-years variations. We explain this based on simple model and prove, that they appear in consequence of 42-years modulation of CW. The excitation ampli es the amplitude of CW for 20 years then damps it for another 20 years. The analysis of the modulated CW signal in a sliding window demonstrates the specific effect, we called the "escargot effect", when instantaneous "virtual" retrograde component appears in the purely prograde (at long-time interval) signal. Chandler excitation envelope shape is similar to this instantaneous retrograde component, which re ects the changes of ellipticity of the approximation ellipse.

This study investigates the relationship between the equatorial atmospheric angular mo- mentum oscillation in the non-rotating frame and lunar tidal potential. Between 2 and 30 days, the corresponding equatorial component is mostly constituted of prograde circular motions, especially of a harmonic at 13.6 days, and of a weekly broad band variation. A simple equilibrium tide model explains the 13.6-day pressure term as result of the lunar tide; the tidal lunar origin of the whole band from 2 to 30 days is attested by speciØc features, not occurring for seasonal band dominated by the solar thermal effect

Observed polar motion consists of uniform circular motions at both positive (prograde) and negative (retrograde) frequencies. Generalized Euler–Liouville equations of Bizouard, taking into account Earth's triaxiality and asymmetry of the ocean tide, show that the corresponding retrograde and prograde circular excitations are coupled at any frequency. In this work, we reconstructed the polar motion excitation in the Chandler band (prograde and retrograde). Then we compared it with geophysical excitation, filtered out in the same way from the series of the Oceanic Angular Momentum (OAM) and Atmospheric Angular Momentum (AAM) for the period 1960–2000. The agreement was found to be better in the prograde band than in the retrograde one.

Chandler wobble amplitude have been decreasing in 2010s as in 1930s. We try to predict its future behaviour through prediction of its complex envelope. The excitation of the Chandler wobble (ChW) reconstructed by Panteleev's ¯lter was also analized. The equation for the complex envelope propagation through the Euler-Liouville equation was derived. Similarities with the climate change characteristics are discussed.

Multichannel singular spectrum analysis (MSSA) is applied to the globally gridded oceanic angular momentum (OAM) data from ECCO (KF080) model, Atmospheric Angular Momentum from ECMWF model, and Earth gravity field from GRACE satellites. Principal components of the oceanic, atmospheric, and hydrological changes and their influence on the rotation of the Earth (polar motion PM and length of day LOD) are extracted. The regions where mass and motion terms make the largest input into PM excitation and LOD changes are identified. The trends, annual, and other global-scale modes are separated. Multichannel singular spectrum analysis is found to be a promising method for signal filtering and modes decomposition. Possible connections between climate change and Earth rotation are discussed.

As the participants of Earth Orientation Parameters Combination of Prediction Pilot Project (EOPC PPP), Sternberg Astronomical Institute of Moscow State University (SAI) and Shanghai Astronomical Observatory (SHAO) have accumulated ∼1800 days of Earth Orientation Parameters (EOP) predictions since 2012 till 2017, which were up to 90 days into the future, and made by four techniques: auto-regression (AR), least squares collocation (LSC), and neural network (NNET) forecasts from SAI, and least-squares plus auto-regression (LS + AR) forecast from SHAO. The predictions were finally combined into SAI-SHAO COMB EOP prediction. In this work we present five-year real-time statistics of the combined prediction and compare it with the uncertainties of IERS bulletin A predictions made by USNO.

This study investigates the relationship between the equatorial atmospheric angular momentum oscillation in the nonrotating frame and the quasi-diurnal lunar tidal potential. Between 2 and 30 days, the corresponding equatorial component, called Celestial Atmospheric Angular Momentum (CEAM), is mostly constituted of prograde circular motions, especially of a harmonic at 13.66 days, a sidelobe at 13.63 days, and of a weekly broadband variation. A simple equilibrium tide model explains the 13.66 day pressure term as a result of the O1 lunar tide. The powerful episodic fluctuations between 5 and 8 days possibly reflect an atmospheric normal mode excited by the tidal waves Q1 (6.86 days) and *σ*1 (7.095 days). The lunar tidal influence on the spectral band from 2 to 30 days is confirmed by two specific features, not occurring for seasonal band dominated by the solar thermal effect. First, Northern and Southern Hemispheres contribute equally and synchronously to the CEAM wind term. Second, the pressure and wind terms are proportional, which follows from angular momentum budget considerations where the topographic and friction torques on the solid Earth are much smaller than the one resulting from the equatorial bulge. Such a configuration is expected for the case of tidally induced circulation, where the surface pressure variation is tesseral and cannot contribute to the topographic torque, and tidal winds blow only at high altitudes. The likely effects of the lunar-driven atmospheric circulation on Earth's nutation are estimated and discussed in light of the present-day capabilities of space geodetic techniques.

Let k be a field of characteristic zero, let G be a connected reductive algebraic group over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k- rational functions on G, respectively, g. The conjugation action of G on itself induces the adjoint action of G on g. We investigate the question whether or not the field extensions k(G)/k(G)^G and k(g)/k(g)^G are purely transcendental. We show that the answer is the same for k(G)/k(G)^G and k(g)/k(g)^G, and reduce the problem to the case where G is simple. For simple groups we show that the answer is positive if G is split of type A_n or C_n, and negative for groups of other types, except possibly G_2. A key ingredient in the proof of the negative result is a recent formula for the unramified Brauer group of a homogeneous space with connected stabilizers. As a byproduct of our investigation we give an affirmative answer to a question of Grothendieck about the existence of a rational section of the categorical quotient morphism for the conjugating action of G on itself.

Let G be a connected semisimple algebraic group over an algebraically closed field k. In 1965 Steinberg proved that if G is simply connected, then in G there exists a closed irreducible cross-section of the set of closures of regular conjugacy classes. We prove that in arbitrary G such a cross-section exists if and only if the universal covering isogeny Ĝ → G is bijective; this answers Grothendieck's question cited in the epigraph. In particular, for char k = 0, the converse to Steinberg's theorem holds. The existence of a cross-section in G implies, at least for char k = 0, that the algebra k[G]G of class functions on G is generated by rk G elements. We describe, for arbitrary G, a minimal generating set of k[G]G and that of the representation ring of G and answer two Grothendieck's questions on constructing generating sets of k[G]G. We prove the existence of a rational (i.e., local) section of the quotient morphism for arbitrary G and the existence of a rational cross-section in G (for char k = 0, this has been proved earlier); this answers the other question cited in the epigraph. We also prove that the existence of a rational section is equivalent to the existence of a rational W-equivariant map T- - - >G/T where T is a maximal torus of G and W the Weyl group.

This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.