Polesrigid

Polesrigid is a term used in theoretical discussions to describe a form of rigidity tied to the singularities, or poles, of certain complex-analytic or transfer-like objects. In this view, a system is polesrigid if its pole data—locations, orders, and principal parts—remain invariant under a prescribed class of deformations. Such invariance implies that the configuration of singularities acts as a rigid backbone for the object, constraining how the system can vary without altering essential features.

Formally, let f be a meromorphic function on a fixed domain with a finite pole set P = {p1, ..., pn}. The object is polesrigid with respect to a deformation family D if, for every deformation d in D that preserves P and the principal parts of f at each pole, the deformed function f∘d is equivalent to f under a domain automorphism that fixes P. In other words, the pole data is an invariant under D.

Polesrigidity is discussed in areas such as complex dynamics, spectral theory, and certain network models where resonances play the role of poles. It contrasts with flexible or moduli-type descriptions where pole positions can vary widely. Typical examples are restricted families of rational or meromorphic functions where the pole locations are fixed by construction, and only non-pole data is allowed to vary within tight constraints.

Although not universally standardized, the concept provides a language for talking about systems where singular behavior anchors the overall structure. Related topics include rigidity, pole theory, and meromorphic dynamics.