Final Answer:
The provided assertion "The correct answer is False
Step-by-step explanation:
In order for a map to have two fixed points, one being a sink and the other a saddle, the eigenvalues associated with the fixed points must satisfy certain conditions. Specifically, for a sink, the eigenvalues must have negative real parts, indicating stability, while for a saddle, there must be at least one eigenvalue with a positive real part, indicating instability. If there are two fixed points, one of each type, the system is a saddle-sink system.
However, this condition is not enough to uniquely determine the range of parameters (a) that satisfies it. The specific values of (a) will depend on the details of the map or the dynamical system in question. Therefore, the statement is generally false because without additional information about the map, we cannot precisely specify the range of parameters (a) for which the system exhibits a saddle-sink behavior.
In summary, while it is true that a dynamical system can have two fixed points with one being a sink and the other a saddle, the range of parameters (a) determining this behavior cannot be definitively stated without further details about the specific map or system under consideration. Hence, the correct answer is "False."