Orbits of Martin's Map

map parameters

a

0.5

b

-0.5

c

0.5

randomize a, b, c

number of iterates

n

2000

4000

8000

hide locators

full range

⊕

This is the two-dimensional map known as Martin's map:

x

k+1

=

y

k

-sgn(

x

k

)

b

x

k

-c

,

y

k+1

=a-

x

k

.

Orbits are generated by iterating the map

n

times using different initial points. The map parameters

a

,

b

, and

c

can be varied manually or a random set can be launched. Three orbits are plotted initially, starting from three different initial points marked by locator objects "

⊕

". You can drag these initial points or add and/or delete new ones (Alt+Click on Windows) inside the plot. Three orbit colors are used cyclically.