General :: Recursive Searching Files In Directory Matching Given Name?

I am writing a shell script that finds all files named <myFile> in a directory <dir> or any of its subdirectories, recursively. I also need to take care of symbolic links that may form cycles, to avoid infinite loops. I am not supposed to use find command for the same

I started writing the code but got stuck. I thought using recursion may be a smart way, but its not working.

Code:
#!/bin/sh
findFiles()
{
thisDIR=$1
#cd $thisDIR
code....