Geometric fuzzification

Abstract unavailable at this time... Mathematics Subject Classification (2000): 03E72, 52A01, 54E35, 53C70, 14M15 Quaestiones Mathematicae 25 (2002), 147-16

Quadratic Hamilton–Poisson systems on se(1,1)∗− : the Inhomogeneous case

We consider equivalence, stability and integration of quadratic Hamilton–Poisson systems on the semi-Euclidean Lie–Poisson space se(1,1)∗−. The inhomogeneous positive semidefinite systems are classified (up to affine isomorphism); there are 16 normal forms. For each normal form, we compute the symmetry group and determine the Lyapunov stability nature of the equilibria. Explicit expressions for the integral curves of a subclass of the systems are found. Finally, we identify several basic invariants of quadratic Hamilton–Poisson systems.This research was supported in part by the European Union’s Seventh Framework Programme (FP7/2007-2013, grant no. 317721). The first two authors would also like to acknowledge the financial support of the National Research Foundation (NRF-DAAD) and Rhodes University towards this research. Additionally, the second author acknowledges the financial support of the Claude Leon Foundation.http://link.springer.com/journal/104402019-04-01hj2018Mathematics and Applied Mathematic