Collatz conjecture question

The Collatz conjecture has come up in comp.lang.c, and it got me thinking
about it.

First, I'm not a mathematician, nor do I play one on TV.  But I wanted
to find out if there were any papers or other references that
have discussed the following:

To compute the next number in a series
Odd numbers: N = 3N+1
Even numbers: N = N/2

So it seems that for odd numbers, the next number in the series
will always be even; but for even numbers, the next number might
be odd or even.

And that's what I'm wondering about:  has anyone ever explored
whether or not the even operation would tend to "dominate" a
series, and that is why it eventually arrives at 1?

I don't even know how to express that mathematically.  Hopefully
this isn't too naive a question.  TIA for any pointers one can
provide.

Thanks,

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-v