Maps:  Flows: 
Discrete time  Continuous time 
Variables change abruptly  Variables change smoothly 
Described by algebraic equations  Described by differential equations 
Complicated dynamics (in 1D)  Simple dynamics (in 1D) 
X_{n}_{+1} = f(X_{n})  dx/dt = f(x) 
Example: X_{n}_{+1 }= AX_{n}  Example: dx/dt = ax 
Solution: X_{n}_{ }= A^{n}X_{0}

Solution: x = x_{0}e^{at}

Growth for A >1
Decay for A < 1 
Growth for a > 0
Decay for a < 0 
We call this an "orbit"  We call this a "trajectory" 
n > t, A > e^{a}  t > n, a > log_{e} A 
Spiral point (focus)
if b < 2 (underdamped) 
Radial point (node)
if b > 2 (overdamped) 