The aim of the present paper is to examine the symmetry groups of an autonomous Hamiltonian system. The authors use the classical method of finding point transformations. According to their approach a complete classification for one and two degrees of freedom is presented as well as partial results for the case of three degrees of freedom. In general it is obtained a maximal dimension for the harmonic oscillator or a free particle while the other dimensions vary between 1 and n^2+3. Finally by considering velocity-dependent potentials linear in the momenta it is proved an interesting result concerning the symmetry group of the corresponding Hamiltonian system. (This paper is based on a talk presented by the author in the 4th Panellenic Conference on Geometry on "Research in Geometry and in its Teaching towards the 21st century'' taking place in the University of Patras, Greece, 28--30 May 1999.)

Στοιχεία Άρθρου

Περιοδικό	Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Αρ. Τεύχους	Τεύχος 44
Περίοδος	2000
Συγγραφέας	Christopoulos Sophocleous, Pantelis A. Damianou
Αρ. Αρθρου	10
Σελίδες	87-96
Γλώσσα	-
Λέξεις Κλειδιά	-

Lie point Symmetries of Hamiltonian Systems