Bifurcation of Non-Semi-Simple Zero Eigenvalues at the Critical Point of the Statical Bifurcation of Nonlinear Rotor System

The objective of the study is to discuss the instability of the center subspace of a nonlinear rotor system with gyroscopic, inertial and potential forces, and nonlinear forces of the shaft, whose linear approximation has a m-multiple non-semi-simple zero eigenvalues. That is to discuss how the parameter changes affect the variations of non-semi-simple zero eigenvalues of the center subspace. The Puiseux expansion is used to develop the expressions of variations of non-semi-simple eigenvalues. The method for computing the generalized modes of the center subspace are given, and expression of variations of 2-multiple non-semi-simple zero eigenvalues is transformed into a more convenient form.

ON THE EXISTENCE OF THE PUISEUX EXPANSION OF THE DISCOUNTED REWARDS: A COUNTEREXAMPLE

This note presents an example indicating for denumerable Markov decision chains that nonexistence of the Laurent expansion of the α-discounted rewards in α = 1 implies also nonexistence of the Puiseux expansion.