Given a control system on $SU(n)$ (or any other compact, semi-simple Lie group I suspect) of the form:

$\frac{d U_t}{dt} = (A + w(t)B)U_t$

where $A,B \in \mathfrak{su}(n)$ generate the algebra (to ensure controlability) consider the end-point map:

$V_T[w] = U_T$, the solution to the system's defining equation. Further assume that $T$ is large enough that $V_T$ is a surjective map from the space of controls (I've left this space somewhat flexible to see what is needed) to $SU(n)$, I.e. the attainable set is maximal.

Are the singular critical points of $V_T$ all isolated in control space for generic values of $A,B$ meeting the premises?

Given a control system on $\mathrm{SU}(n)$ (or any other compact, semi-simple Lie group I suspect) of the form:

$\frac{d U_t}{dt} = (A + w(t)B)U_t$

where $A,B \in \mathfrak{su}(n)$ generate the algebra (to ensure controllability) consider the end-point map:

$V_T[w] = U_T$, the solution to the system's defining equation. Further assume that $T$ is large enough that $V_T$ is a surjective map from the space of controls (I've left this space somewhat flexible to see what is needed) to $\mathrm{SU}(n)$, i.e. the attainable set is maximal.

Are the singular critical points of $V_T$ all isolated in control space for generic values of $A,B$ meeting the premises?

Given a control system on $SU(n)$ (or any other compact, semi-simple Lie group I suspect) of the form:

$\frac{d U_t}{dt} = (A + w(t)B)U_t$

where $A,B \in \mathfrak{su}(n)$ generate the algebra (to ensure controlability) consider the end-point map:

$V_T[w] = U_T$, the solution to the system's defining equation. Further assume that $T$ is large enough that $V_T$ is a surjective map from the space of controls (I've left this space somewhat flexible to see what is needed) to $SU(n)$, I.e. the attainable set is maximal.

Are the singular critical points of $V_T$ all isolated in control space for generic values of $A,B$ meeting the premises? I have found numerical evidence to suggest that for 'typical' (i.e. many randomly generated cases) this seems to to be true.

Given a control system on $SU(n)$ (or any other compact, semi-simple Lie group I suspect) of the form:

$\frac{d U_t}{dt} = (A + w(t)B)U_t$

where $A,B \in \mathfrak{su}(n)$ generate the algebra (to ensure controlability) consider the end-point map:

$V_T[w] = U_T$, the solution to the system's defining equation. Further assume that $T$ is large enough that $V_T$ is a surjective map from the space of controls (I've left this space somewhat flexible to see what is needed) to $SU(n)$, I.e. the attainable set is maximal.

Are the singular critical points of $V_T$ all isolated in control space for generic values of $A,B$ meeting the premises?

Given a control system on $SU(n)$ (or any other compact, semi-simple Lie group I suspect) of the form:

$\frac{d U_t}{dt} = (A + w(t)B)U_t$

where $A,B \in \mathfrak{su}(n)$ generate the algebra (to ensure controlability) consider the end-point map:

$V_T[w] = U_T$ the solution to the system's defining equation. Further assume that $T$ is large enough that $V_T$ is a surjective map from the space of controls (I've left this space somewhat flexible to see what is needed) to $SU(n)$, I.e. the attainable set is maximal.

Are the singular critical point of $V_T$ all isolated in control space for generic values of $A,B$ meeting the premises? I have found numerical evidence to surest that for 'typical' (i.e. many randomly generated cases) this seems to to be true.

Given a control system on $SU(n)$ (or any other compact, semi-simple Lie group I suspect) of the form:

$\frac{d U_t}{dt} = (A + w(t)B)U_t$

where $A,B \in \mathfrak{su}(n)$ generate the algebra (to ensure controlability) consider the end-point map:

$V_T[w] = U_T$, the solution to the system's defining equation. Further assume that $T$ is large enough that $V_T$ is a surjective map from the space of controls (I've left this space somewhat flexible to see what is needed) to $SU(n)$, I.e. the attainable set is maximal.

Are the singular critical points of $V_T$ all isolated in control space for generic values of $A,B$ meeting the premises? I have found numerical evidence to suggest that for 'typical' (i.e. many randomly generated cases) this seems to to be true.