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Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem

2018-10-03 Mathematics
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Release : 2018-10-03
Genre : Mathematics
Kind : eBook
Book Rating : 020/5 ( reviews)

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Book Synopsis Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem by : Gabriella Pinzari

Download or read book Perihelia Reduction and Global Kolmogorov Tori in the Planetary Problem written by Gabriella Pinzari. This book was released on 2018-10-03. Available in PDF, EPUB and Kindle. Book excerpt: The author proves the existence of an almost full measure set of -dimensional quasi-periodic motions in the planetary problem with 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.

Global Regularity for 2D Water Waves with Surface Tension

2019-01-08 Capillarity
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Release : 2019-01-08
Genre : Capillarity
Kind : eBook
Book Rating : 033/5 ( reviews)

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Book Synopsis Global Regularity for 2D Water Waves with Surface Tension by : Alexandru D. Ionescu

Download or read book Global Regularity for 2D Water Waves with Surface Tension written by Alexandru D. Ionescu. This book was released on 2019-01-08. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of the authors' analysis is to develop a sufficiently robust method (the “quasilinear I-method”) which allows the authors to deal with strong singularities arising from time resonances in the applications of the normal form method (the so-called “division problem”). As a result, they are able to consider a suitable class of perturbations with finite energy, but no other momentum conditions. Part of the authors' analysis relies on a new treatment of the Dirichlet-Neumann operator in dimension two which is of independent interest. As a consequence, the results in this paper are self-contained.

On Space-Time Quasiconcave Solutions of the Heat Equation

2019-06-10 Heat equation
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Release : 2019-06-10
Genre : Heat equation
Kind : eBook
Book Rating : 241/5 ( reviews)

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Book Synopsis On Space-Time Quasiconcave Solutions of the Heat Equation by : Chuanqiang Chen

Download or read book On Space-Time Quasiconcave Solutions of the Heat Equation written by Chuanqiang Chen. This book was released on 2019-06-10. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors first obtain a constant rank theorem for the second fundamental form of the space-time level sets of a space-time quasiconcave solution of the heat equation. Utilizing this constant rank theorem, they obtain some strictly convexity results of the spatial and space-time level sets of the space-time quasiconcave solution of the heat equation in a convex ring. To explain their ideas and for completeness, the authors also review the constant rank theorem technique for the space-time Hessian of space-time convex solution of heat equation and for the second fundamental form of the convex level sets for harmonic function.

Interpolation for Normal Bundles of General Curves

2019-02-21 Curves, Algebraic
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Release : 2019-02-21
Genre : Curves, Algebraic
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Book Rating : 89X/5 ( reviews)

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Book Synopsis Interpolation for Normal Bundles of General Curves by : Atanas Atanasov

Download or read book Interpolation for Normal Bundles of General Curves written by Atanas Atanasov. This book was released on 2019-02-21. Available in PDF, EPUB and Kindle. Book excerpt: Given n general points p1,p2,…,pn∈Pr, it is natural to ask when there exists a curve C⊂Pr, of degree d and genus g, passing through p1,p2,…,pn. In this paper, the authors give a complete answer to this question for curves C with nonspecial hyperplane section. This result is a consequence of our main theorem, which states that the normal bundle NC of a general nonspecial curve of degree d and genus g in Pr (with d≥g+r) has the property of interpolation (i.e. that for a general effective divisor D of any degree on C, either H0(NC(−D))=0 or H1(NC(−D))=0), with exactly three exceptions.

Multilinear Singular Integral Forms of Christ-Journé Type

2019-02-21 Forms (Mathematics)
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Release : 2019-02-21
Genre : Forms (Mathematics)
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Book Rating : 377/5 ( reviews)

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Book Synopsis Multilinear Singular Integral Forms of Christ-Journé Type by : Andreas Seeger

Download or read book Multilinear Singular Integral Forms of Christ-Journé Type written by Andreas Seeger. This book was released on 2019-02-21. Available in PDF, EPUB and Kindle. Book excerpt:

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