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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.

Using multichannel singular spectrum analysis (MSSA) we decomposed climatic time series into principal components, and compared them with Earth rotation parameters. The global warming trends were initially subtracted. Similar quasi 60 and 20 year periodic oscillations have been found in the global mean Earth temperature anomaly (HadCRUT4) and global mean sea level (GMSL). Similar cycles were also found in Earth rotation variation. Over the last 160 years multi-decadal change of Earth's rotation velocity is correlated with the 60-year temperature anomaly, and Chandler wobble envelope reproduces the form of the 60-year oscillation noticed in GMSL. The quasi 20-year oscillation observed in GMSL is correlated with the Chandler wobble excitation. So, we assume that Earth's rotation and climate indexes are connected. Despite of all the clues hinting this connection, no sound conclusion can be done as far as ocean circulation modelling is not able to correctly catch angular momentum of the oscillatory modes.

Earth's variable rotation is mainly produced by the variability of the atmospheric angular momentum (AAM). In particular, the axial AAM component *χ*3, which undergoes especially strong variations, induces changes in the Earth's rotation rate. In this study we analysed maps of regional input into the effective axial AAM from 1948 through 2011 from NCEP/NCAR reanalysis. Global zonal circulation patterns related to the length of day (LOD) were described. We applied Multichannel Singular Spectrum Analysis (MSSA) jointly to the mass and motion components of AAM, which allowed us to extract annual, semiannual, 4-month, quasi-biennial, 5-year, and low-frequency oscillations. Principal components (PCs) strongly related to El Nino southern oscillation (ENSO) were released. They can be used to study ENSO-induced changes in pressure and wind fields and their coupling to LOD. The PCs describing the trends have captured slow atmospheric circulation changes possibly related to climate variability.

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.