Topic: Deterministic vs Random.
SLIDES for the evening
modular arithmetic
case of 13; 3, 1
Galleries
LCGs : x -> ax + c (mod m)
Doubling Map. x ->2x (mod 1) ; see
dyadic transf. wiki
Fibonacci Maps (mod p) : (x,y) ->( y, x + y ), x, y mod m
Fibonacci Map on the torus : (x,y) ->( y, x + y ), x, y taken from the circle = the real numbers mod 1.
the Fib. map is the `square root' of Arnol'd's Cat map (x,y) ->( 2x + y, x + y ) x, y real numbers mod 1.
the Baker's transformation
Standard Map
Henon Map
Interactive Maps
Motivations
Physics. Newton showed us how to write classical dynamics as differential equations.
To approximates solve an ODE we use difference eqsn, so MAPS. to maps