Fixed Point Index

The fixed point index is a mathematical tool that measures how a function behaves around points where it maps back to itself (fixed points). Think of it as counting fixed points with a sense of their stability or importance: a positive index indicates the fixed point is stable or influential, while a negative index suggests instability. Essentially, it helps us understand whether fixed points exist and how the function behaves near them, providing insight into the structure and dynamics of the system being studied.