1.

Record Nr.

UNINA9910793296803321

Autore

Pinzari Gabriella <1966->

Titolo

Perihelia reduction and Global Kolmogorov tori in the planetary problem / / Gabriella Pinzari

Pubbl/distr/stampa

Providence, Rhode Island : , : American Mathematical Society, , [2018]

©2018

ISBN

1-4704-4813-0

Descrizione fisica

1 online resource (104 pages)

Collana

Memoirs of the American Mathematical Society ; ; Number 1218

Disciplina

521

Soggetti

Celestial mechanics

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

"September 2018. Volume 255. Number 1218 (first of 7 numbers)."

Nota di bibliografia

Includes bibliographical references.

Nota di contenuto

Background and results -- Kepler maps and the Perihelia reduction -- The P-map and the planetary problem -- Global Kolmogorov tori in the planetary problem -- Proofs.

Sommario/riassunto

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.



2.

Record Nr.

UNINA9910350249103321

Titolo

Algebraic Topology and Related Topics / / edited by Mahender Singh, Yongjin Song, Jie Wu

Pubbl/distr/stampa

Singapore : , : Springer Nature Singapore : , : Imprint : Birkhäuser, , 2019

ISBN

981-13-5742-0

Edizione

[1st ed. 2019.]

Descrizione fisica

1 online resource (XIII, 313 p. 73 illus., 10 illus. in color.)

Collana

Trends in Mathematics, , 2297-024X

Disciplina

514.2

Soggetti

Algebraic topology

Functional analysis

Algebraic Topology

Functional Analysis

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Nota di contenuto

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.

Sommario/riassunto

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



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.