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Record Nr. |
UNINA9910793296803321 |
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Autore |
Pinzari Gabriella <1966-> |
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Titolo |
Perihelia reduction and Global Kolmogorov tori in the planetary problem / / Gabriella Pinzari |
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Pubbl/distr/stampa |
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Providence, Rhode Island : , : American Mathematical Society, , [2018] |
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©2018 |
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ISBN |
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Descrizione fisica |
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1 online resource (104 pages) |
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Collana |
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Memoirs of the American Mathematical Society ; ; Number 1218 |
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Disciplina |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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"September 2018. Volume 255. Number 1218 (first of 7 numbers)." |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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Background and results -- Kepler maps and the Perihelia reduction -- The P-map and the planetary problem -- Global Kolmogorov tori in the planetary problem -- Proofs. |
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Sommario/riassunto |
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The author proves the existence of an almost full measure set of (3n-2)-dimensional quasi-periodic motions in the planetary problem with (1+n) masses, with eccentricities arbitrarily close to the Levi-Civita limiting value and relatively high inclinations. This extends previous results, where smallness of eccentricities and inclinations was assumed. The question had been previously considered by V. I. Arnold in the 1960s, for the particular case of the planar three-body problem, where, due to the limited number of degrees of freedom, it was enough to use the invariance of the system by the SO(3) group. The proof exploits nice parity properties of a new set of coordinates for the planetary problem, which reduces completely the number of degrees of freedom for the system (in particular, its degeneracy due to rotations) and, moreover, is well fitted to its reflection invariance. It allows the explicit construction of an associated close to be integrable system, replacing Birkhoff normal form, a common tool of previous literature. |
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2. |
Record Nr. |
UNINA9910350249103321 |
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Titolo |
Algebraic Topology and Related Topics / / edited by Mahender Singh, Yongjin Song, Jie Wu |
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Pubbl/distr/stampa |
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Singapore : , : Springer Nature Singapore : , : Imprint : Birkhäuser, , 2019 |
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ISBN |
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Edizione |
[1st ed. 2019.] |
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Descrizione fisica |
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1 online resource (XIII, 313 p. 73 illus., 10 illus. in color.) |
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Collana |
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Trends in Mathematics, , 2297-024X |
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Disciplina |
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Soggetti |
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Algebraic topology |
Functional analysis |
Algebraic Topology |
Functional Analysis |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Chapter 1. Homological infinity of 4D universe for every 3-manifold -- Chapter 2. On the exponents of $[J(X), \Omega (Y)]$ -- Chapter 3. Nielsen theory on the nilmanifold $\Gamma_{m+1}\backslash\mathrm{Heis}^{m+1}$ of the generalized Heisenberg group $\mathrm{Heis}^{m+1}$ -- Chapter 4. Vector field problem for homogeneous spaces -- Chapter 5. Lickorish type classification of closed manifolds over simple polytopes -- Chapter 6. Stable and unstable stratifications on classifying spaces of acyclic categories -- Chapter 7. Equivariant cohomology of torus orbifolds with two vertices -- Chapter 8. Free torus actions on products of Milnor manifolds -- Chapter 9. The cohomology classes of a point and the diagonal in flag manifolds -- Chapter 10. On a construction for the generators of the polynomial algebra as a module over the Steenrod algebra -- Chapter 11. KO-groups of stunted complex and quaternionic projective spaces -- Chapter 12. Homotopy groups of (n-1)-connected (2n + 1)-manifolds -- Chapter 13. A note on the topology of polygonal spaces -- Chapter 14. Generalized unknotting number of virtual links. |
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Sommario/riassunto |
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This book highlights the latest advances in algebraic topology, from homotopy theory, braid groups, configuration spaces and toric topology, to transformation groups and the adjoining area of knot |
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theory. It consists of well-written original research papers and survey articles by subject experts, most of which were presented at the “7th East Asian Conference on Algebraic Topology” held at the Indian Institute of Science Education and Research (IISER), Mohali, Punjab, India, from December 1 to 6, 2017. Algebraic topology is a broad area of mathematics that has seen enormous developments over the past decade, and as such this book is a valuable resource for graduate students and researchers working in the field. |
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