We give a general procedure for the calculation of the intersection Poincaré polynomial of the symplectic quotient M/K, of a symplectic manifold M by a hamiltonian group action of a compact Lie group K. The procedure mirrors that used by Kirwan for the calculation of the intersection Poincaré polynomial of a geometric invariant theory quotient of a nonsingular complex projective variety. That i...

0. Introduction We consider (possibly infinite dimensional) Lie algebras over a fixed field k of characteristic zero. Let g be a Lie algebra, S = Sg and U = Ug the symmetric and universal enveloping algebras, and F ⊂ F ⊂ · · · ⊂ U the coalgebra filtration F := k + g + g · · · + g. Recall that the Poincaré-Birkhoff-Witt isomorphism between S and the associated graded ring GFU is induced by the s...

The reconnection process in the dynamics of cubic nontwist maps, introduced in [3], is studied. The present paper extends the work presented in [8]. As in that work, in order to describe the route to reconnection of the involved Poincaré–Birkhoff chains or dimerised chains we investigate an approximate interpolating Hamiltonian of the map under study revealing again that the scenario of reconne...

In the development of magnetic fusion reactors which will be the source for future low cost power physicists must be able to analyze the magnetic fields that confine the burning plasma. The corresponding magnetic fieldlines have a periodic or quasi-periodic behavior. In this paper we describe a simple and efficient geometric technique that allows for effective visualization and topological anal...

The dynamics of the Poincaré map, associated with a periodic tridiagonal system modeling cooperative-competitive ecological interactions, has been investigated. It is shown that the limit-set is either a fixed point or is contained in the boundary of the positive cone and itself contains a cycle of fixed points. Furthermore, the dynamics is trivial if the number of interactive species is not gr...

A very simple nonlinear parallel forced LCR circuit is proposed as Balamurugan-Sengodan-Daniel (BSD) circuit includes linear inductors, capacitor, locally active resistor and a diode driven by a sinusoidal voltage source. By varying the amplitude of the external signal, we identify the familiar quasiperiodic routes to chaos as well as period doubling sequences, windows, and so on. The performan...

This paper discusses the domain of attraction and its sensitivity for a class of chaotic attractors generated by using second-order linear systems with hysteresis-series. It is found that the domain of attraction of the chaotic attractors is determined by an unstable limit cycle. The chaotic dynamical behaviors are demonstrated by using the Poincaré map. The sensitivity of the domain of attract...

The aim of our paper is to provide a new class of five-phase anti-lock brake algorithms (that use wheel deceleration logic-based switching) and a simple mathematical background that explains their behavior. Firstly, we completely characterize the conditions required for our algorithm to work. Secondly, we explain how to compute analytically an approximation of the Poincaré map of the system (wi...

The connection between symmetries and linearizations of discrete-time dynamical systems is being inverstigated. It is shown, that existence of semigroup structures related to the vector field and having linear representations enables reduction of linearization problem to a system of first order partial differential equations. By means of inverse of the Poincaré map one can relate symmetries in ...

Nonautonomous systems with periodic solutions are encountered frequently in applications. In this paper, we will consider simple systems whose solutions are periodic with a known period. Their transformation under linearized collocation methods is investigated, using a technique called stroboscopic sampling, a discrete version of the well-known Poincaré map. It is shown that there is an inextri...