k-integrals and k-Lie symmetries in discrete dynamical systems

Lie Point Symmetries and First Integrals: the Kowalevsky Top

We show that Lie group analysis yields the first integrals admitted by any system of ordinary differential equations if the method developed by Nucci (J.) is applied. As an example, we obtain the famous first integral of the Kowalevsky top.

Quantum Symmetries and K-Theory

Modified from Vienna Lectures August 2014 for PiTP, July 2015. VERY ROUGH VERSION: UNDER CONSTRUCTION. Version: July 23, 2015

Symmetries of discrete dynamical systems involving two species

Lie discrete symmetries of lattice equations

We extend two of the methods previously introduced to find discrete symmetries of differential equations to the case of difference and differentialdifference equations. As an example of the application of the methods, we construct the discrete symmetries of the discrete Painlevé I equation and of the Toda lattice equation.

study of bifurcation and hyperbolicity in discrete dynamical systems

bifurcations leading to chaos have been investigated in a number of one dimensional dynamical systems by varying the parameters incorporated within the systems. the property hyperbolicity has been studied in detail in each case which has significant characteristic behaviours for regular and chaotic evolutions. in the process, the calculations for invariant set have also been carried out. a bro...