Elementary Differential Topology
An autonomous system refers to a type of differential equation system where the derivatives of the variables depend only on the variables themselves and not explicitly on time. This means that the behavior of the system is governed entirely by its current state, which leads to the concept of integral curves representing solutions that evolve over time based on initial conditions. This idea is closely tied to the flow of the system, where the paths traced by solutions reveal insights into the system's dynamics.
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