The Terras map is the accelerated form of the map in the Collatz conjecture, defined on the positive integers by
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(1)
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It combines an odd Collatz step with the division by 2 that necessarily follows it. Consequently, an orbit of the Terras map reaches 1 iff the corresponding Collatz orbit reaches 1.
Terras (1976, 1979) used this map to study stopping times and proved the existence of limiting densities for integers with bounded stopping time.
Problem and Its Generalizations." Amer. Math. Monthly 92,
3-23, 1985.Terras, R. "A Stopping Time Problem on the Positive
Integers." Acta Arith. 30, 241-252, 1976.Terras,
R. "On the Existence of a Density." Acta Arith. 35, 101-102,
1979.