Does the elliptical orbit have many periapsis points?

If I have the position and velocity vectors of a satellite in an elliptical orbit for one point in time, then I can know its position in its orbit at any other time, and with that I can calculate the minimum altitude from the center of earth and the time it occurs.

Can we say here that we will get many similar minimum altitudes? Which means many periapsis points? In other words, can we say that the we have many periapsis points each point appears during a one complete rotation of the satellite around earth?