Nonlinear ordinary differential equations: A discussion on symmetries and singularities Page 1
International Journal of Geometric Methods in Modern Physics Vol. 13, No. 7 (2016) 1630009 …

The characteristic feature of the Kepler Problem is the existence of the so-called Laplace—
Runge—Lenz vector which enables a very simple discussion of the properties of the orbit for …

We present a short history of the Ermakov Equation with an emphasis on its discovery by the
West and the subsequent boost to research into invariants for nonlinear systems although …

We generalize the two-dimensional autonomous Hamiltonian–Kepler–Ermakov dynamical
system to three dimensions using the sl (2, R) invariance of Noether symmetries and …

Non-central forces have a wide variety of applications in classical and quantum mechanics
as demonstrated in this book. The author emphasizes the study of time-dependent …

We review some recent results of the theory of Lie systems in order to apply such results to
study Ermakov systems. The fundamental properties of Ermakov systems, ie their …

Актуальность темы. Данная работа посвящена аналитическому и алгебраическому
исследованию проблемы интегрируемости обыкновенных дифференциальных …

A canonical Hamiltonian formalism is derived for a class of Ermakov systems specified by
several different frequency functions. This class of systems comprises all known cases of …

In the present work, we survey various methodsused for the construction of exact invariants
fordynamical systems involving an explicit time dependence. More stress is placed on two …

The symmetry analysis of Ermakov systems is extended to the generalized case where the
frequency depends on the dynamical variables besides time. In this extended framework, a …