After examining the influence of Turkish tribes in Persia, Anatolia and India, what inspired these tribes to enter these areas? My text is Bentley and Ziegler's Traditions & Encounters.
In your text, there is a subsection entitled “Turkish Empires in Persia, Anatolia, and India.” In addition to reading this answer, it would be a good idea for you to consult that part of your text to get more details on this topic.
The authors say that the Turkish peoples entered the areas that you mention “at different times and for different purposes” (p. 268 of the Brief Second Edition). Looking first at their entry into Persia, we can see that it was done for much the same reasons that inspired the Germanic tribes to enter the Roman Empire. The Turkish peoples lived on the outskirts of the Abbasid Empire in Persia. They could see that this empire was stronger and richer than they were. Accordingly, they wanted to be part of it. They started to take service in the Abbasid armies and were thus able to come and live in the empire. In this way, they started to move into Persia.
By contrast, when the Turks entered Anatolia and India, they did so from a position of power. They had already become very powerful in the Abbasid Empire, becoming the effective rulers of that empire. Once they had accomplished this, they wanted to expand. This is what led them to move into Anatolia and India. In Anatolia, they started to migrate in large numbers and then defeated the Byzantine forces at Manzikert, paving the way for even more Turks to enter. By contrast, their entrance into India started as a series of raids meant only to gain plunder. After that, they became more interested in taking permanent power over the area.
Thus, the Turks entered these three areas at different times and for somewhat different reasons.