Andronikos Paliathanasis
PhD Thesis
Title: Symmetries of Differential Equations with Applications in Relativistic Physics
Abstract: In this thesis, we study the one parameter point transformations which leave invariant the differential equations. In particular we study the Lie and the Noether point symmetries of second order differential equations. We establish a new geometric method which relates the point symmetries of the differential equations with the collineations of the underlying manifold where the motion occurs. This geometric method is applied in order the two and three dimensional Newtonian dynamical systems to be classified in relation to the point symmetries; to generalize the Newtonian Kepler-Ermakov system in Riemannian spaces; to study the symmetries between classical and quantum systems and to investigate the geometric origin of the Type II hidden symmetries for the homogeneous heat equation and for the Laplace equation in Riemannian spaces. At last but not least, we apply this geometric approach in order to determine the dark energy models by use the Noether symmetries as a geometric criterion in modified theories of gravity.Supervisor: Prof. Michael Tsamparlis
Advisors: Dr. Spyros Basilakos and Dr. Christos Efthimiopoulos
Examiners: Prof. S. Capozziello, Prof. P.J. Ioannou, Prof. T. Apostolatos and Prof. A.H. Kara
Date of Exam: 24 June 2014
Presentation: .pdf
Thesis: .pdf
Recent Publications
A. Borowiec, S. Capozziello, M. De Laurentis, A. Paliathanasis, M. Paolella and A. Wojnar,
Invariant solutions and Noether symmetries in Hybrid Gravity, to be published in PRD, (arXiv:1407.4313)
A. Paliathanasis, M. Tsamparlis and M.T. Mustafa,
Symmetry analysis of the Klein-Gordon equation in Bianchi I spacetimes, to be published in IJGMMP (2015), (arXiv:1411.0398)
A. Paliathanasis, M. Tsamparlis and S. Basilakos,
Dynamical symmetries and observational constraints in scalar field cosmology,
Phys. Rev. D 90, 103524 (2014), (arXiv:1410.4930)
A. Paliathanasis and M. Tsamparlis,
Two scalar field cosmology: Conservation laws and exact solutions, Phys. Rev. D 90, 043529 (2014), (arXiv:1408.1798)
M. Tsamparlis, A. Paliathanasis and A. Qadir,
Noether symmetries and isometries of the minimal surface Lagrangian under constant volume in a Riemannian space, IJGMMP (2015) (arXiv:1407.4601)