The Theoretical Minimum Classical Mechanics Solutions L01E03 J. Silva 12 January 2023 Lecture 1: Simple Dynamical Systems and the space of States Exercise 3: Determine which of the dynamical laws shown in equations (2) through to (5) are allowable. A permissible state that shifts the marker one unit in the negative direction at each time step. A permissible state that shifts the marker two units in the positive direction at each time step. A permissible state that shifts the marker a squared unit in the positive direction at each time step. An integer of value 1 to the power of another integer will always be 1, and multiplying that by the integer n will just shift the marker “n” in the positive direction. Since the entire system is multiplied through by -1, surely this state is permissible by shifting the marker “n” in the negative direction at each time step? N ( n + 1 ) = N ( n ) − 1 N ( n + 1 ) = N ( n ) + 2 N ( n + 1 ) = N ( n ) 2 N ( n + 1 ) = − 1 N ( n ) N ( n )