I moti quasi periodici e la stabilità del sistema solare. 1, Dagli epicicli al punto omoclino di Poincaré
Articolo
Data di Pubblicazione:
2007
Citazione:
I moti quasi periodici e la stabilità del sistema solare. 1, Dagli epicicli al punto omoclino di Poincaré / A. Giorgilli. - In: BOLLETTINO DELL'UNIONE MATEMATICA ITALIANA. A. - ISSN 0392-4033. - 10:1(2007 Dec), pp. 465-495.
Abstract:
The problem of stability of planetary motion is revisited with the aim of illustrating some emerging aspects from the historical
development of our knowledge. The note is divided in two parts.
The first one is concerned with the classical methods and ends up with the work of Poincar\'e. The second one deals with the
discoveries of the last 50 years.
The first part of the note starts with the attempts to represent the
motions of the planets as being quasiperiodic, actually by means of
epicicles as in the classical theories. In this framework the
Lindststedt's expansion method is illustrated by applying it to
Duffing's equation. This introduces the main problem of classical
astronomy, namely the role of resonances that shows up in either form
of secular terms or of small divisors in the series expansions of the
solutions of the equation. Then the discovery of the chaotic
behaviour of orbits by Poincar\'e is recalled by illustrating in some
detail the phenomenon of homoclinic intersections.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Sistema solare ; Sistema planetario ; Astronomia
Elenco autori:
A. Giorgilli
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