@dharr Your suggestion would save a lot of computation. Thanks for this.

@Ronan Thank you for your attention and your reference. I'm afraid the contents of the paper you referenced is far over my head. However I will continue to explore this subject. 

@Carl Love From the referenced text by Brannan et. al.;

(The procedure rho) is the hyperbolic reflection (of point z) in the hyperbolic line that is part of a Euclidean circle with centre alpha.

How can the Mobius transformation in rho calculate a hyperbolic reflection of a point without requiring input of a radius of the circle referred to? Are not both a centre and a radius required to define the hyperbolic line of reflection?

My procedure InversePtMobius does require both of these inputs and only reproduces the output of procedure rho when InversePtMobius a centre of alpha and a radius of 1. This is why it seems to me that procedure rho assumes a radius of 1. 

*** I just realized that any given centre of the circle mentioned above implies its radius under the condition that the circle meets the Poincare disk at right angles. ***

I therefore withdraw my Maple Primes question

@Thomas Richard 

@mmcdara I have examined your reply to my question and admire your logic.

I have one question.

Apparently the correct animation requires that the pursuer velocity V__P be a specific ratio of the target velocity V__T.

I tried executing the logic using a slightly different ratio and the pursuers stopped short of capturing the target.

Why this specific ratio required and how did you find it?

@Rouben Rostamian   I would award your and mmcdara's answers both with the trophy, I am greatly impressed with both of them!

@mmcdara I would award your and Rouben's answers both with the trophy, they  both are so clever.

@Rouben Rostamian  

@Carl Love 

@Carl Love and to dharr,

Apparently Maple Primes only allows one reply if I my first view of answers includes two of them.

To dharr: Your answer gives me the incentive to begin learning GraphTheory about which I currently know nothing. I am grateful for this.

To Carl Love: Over the years, among all the experts, it seems to me that your answers show the deepest knowledge of Maple's capabilities. I will strive to understand and benefit from this one. I regret I could not also select your answer at the best one.

@acer Both of your methods are enlightening for me. I will study them further. Thank you for this.

@acer I ran your file_search code against my all purpose folder containing 1017 files, most of which are Maple worksheets. In about 10 minutes it found 28 worksheets containing the phrase "events" and listed their names.

It also emitted about 30 warning messages reading:

"Warning, if d is meant to be the differential symbol (and not just a variable d), use command completion or palettes to enter this expression"

Your code did exactly what I wanted!

Unfortunately, at this time I can't select yours as the best reply.

@acer I hope the other suggesters reply to your latest comment.

@acer At the moment I am busy with another project, so it will be some time before I can try your suggestion. I confirm that am needing a search of 2D input.

On first impression, among the other replies received, I like yours best because it is all within Maple and because you have taken the trouble to originate it.

@gkokovidis Thank you for your suggestion. Now that I have received a number of suggestions, it may take some time for me to try this and I'll report back to you when I do