What does "Bifurcation Set" mean?

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A bifurcation set is a concept used in mathematics to describe a special collection of points where changes occur in the behavior of a system. These points help to understand how different situations or conditions can lead to different outcomes.

In simple terms, imagine a point where a path can split into two or more paths. This can happen in various scenarios, like how a river forks into different streams or how a decision leads to multiple choices. The bifurcation set helps identify where these splits happen and what effects they have on the overall system.

In the study of shapes, particularly in three-dimensional space, bifurcation sets can also relate to how certain shapes are formed and how they behave when viewed from different angles. Understanding these sets can provide insights into the properties of these shapes and how they interact with their surroundings.