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How are Centaur objects linked to the Kuiper belt and short-period comets?

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Illustration showing the eight planets of the solar system in order from the Sun-Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune-depicted to scale by size, with labeled diameters in miles and kilometers. The Sun is partially visible on the left for comparison. — Solar system The planets (in comparative size) in order of distance from the Sun.

Centaur objects serve as a critical evolutionary link between the Kuiper belt and short-period comets. This connection is defined by the following dynamical process:

Origin: Centaurs are icy bodies that originate in the Kuiper belt, a vast reservoir of comet nuclei located beyond the orbit of Neptune.12
Transition: Through gravitational perturbations—primarily by Neptune—these objects are pulled from their stable, distant orbits into the planetary region of the solar system. Once they enter this region, they are classified as Centaurs.13
Evolution: Centaurs travel in unstable, chaotic orbits that cross the paths of the giant planets. Because these orbits are temporary, Centaurs are considered to be in a transitional state; they are either eventually ejected from the solar system, collide with a planet or the Sun, or evolve into short-period comets.245

In essence, Centaurs represent the intermediate stage of a journey where Kuiper belt objects are "handed down" through the giant planets until they reach the inner solar system as active, short-period comets.35