  For Cartan geometries admitting automorphisms with isotropies satisfying a
particular, loosely dynamical property on their model geometries, we
demonstrate the existence of an open subset of the geometry with trivial
holonomy. This property, which generalizes characteristics of isotropies
corresponding to isolated higher-order fixed points in parabolic geometries
that are known to require a nearby open subset to have vanishing curvature,
only relies upon the behavior of the isotropy in the model geometry, and
therefore applies regardless of initial curvature assumptions, such as
regularity or normality. Along the way to proving our main results, we also
derive a couple of results for working with holonomy, relating to limits of
sequences of developments and the existence of antidevelopments, that are
useful in their own right. To showcase the effectiveness of the techniques
developed, we use them to completely characterize all almost c-projective and
almost quaternionic structures that admit a nontrivial automorphism with a
higher-order fixed point, as well as all nondegenerate partially integrable
almost CR structures that admit a higher-order fixed point with non-null
isotropy.
