Trace of the Monodromy Matrix of an Irregular Singular Point of a Linear System of First-Order Ordinary Differential Equations

Key Points

• The formula for the trace of the monodromy matrix is derived for singular points in linear systems.
• This formulation applies to differential equations of pole type and algebraic branch points.
• Analysis includes a special case that exemplifies the general formula derived for specific systems.
• Results may enable deeper understanding of the behavior of differential equations near singular points.

Abstract