Some Perspective As To Holomorphic Flow

Let us take into consideration -- a flow of a suppositional particle, that is being mapped-out over a planar surface, over time.  If one considers the initial straight-bearing movement of the here given arbitrary particle to be arbitrarily moving in a directoral-based topological sway, that would here have a relative rise that is equal to its relative run -- then, the so-eluded-to initial path of the said particle of this case -- would be moving in the course of what may be termed of here as a given arbitrary example of a Hamiltonian operator, that is undergoing the Laplacian-based tracing of an identity function.  So, this so-mentioned "straight-bearing" motion of the given arbitrary particle of such a case, may be considered to be here following a closest-fitting mean-based path -- that is here moving in a hermitian manner, that is equally mapping-out in the relative antiholomorphic direction (to the relative right as to a respective given arbitrary observer) to the same even flow as it is being mapped-out in the norm-to-forward-holomorphic direction (to the relative top as to a respective given arbitrary observer).  This so-described initial-based path of the said particle of this case, will be of a unitary Lagrangian, and in a theoretically completely linear-based manner.  After a certain scalar magnitude of the mappable tracing of the integration of the directly corresponding integration of Laplacian-based states -- that may here work to consider the point at which the so-stated particle in question will perturbate into a clearly different direction -- the particle will then be translated at a subtended genus of an angle of 45 degrees, as sort of an inverse of the initial genus of an identity-based function, yet, this "inversion" will be of a movement in a hermitian manner, that is equally mapping-out in the relative holomorphic direction (to the relative left as to a respective given arbitrary observer) to the same even flow as it is being mapped-out in the norm-to-forward-holomorphic direction (to the relative top as to a respective given arbitrary observer).  Each of such unitary-based Lagrangian paths of this respective given arbitrary example, is separated by what may be thought of here as a Lagrangian-based Chern-Simmons singularity.  Let us now consider the horizontal axis of such a mappable tracing to be of the x based axial of this case, and, let us, as well, consider the vertical axis of such a mappable tracing to be of the y based axial.  Let us then consider the initial situation of which I have described of, as happening in the positive x region.  Now, let us say that  one were to form a trivially isomorphic theoretical topological stratum -- that is to be mapped-out in the negative x region.  This would work to form a theoretical region -- to where the particle-- if it were to intrinsically tend to refract or reflect at 90 at each of its exterior Neumman boundary limits -- would act as a phenomenology, that would here tend to move at its best, to bear a Hamiltonian operand, that would "try" to best fit an ideal mean Lagrangian-based path, over time.  To Be Continued!  Sam Roach.