
The Chirikov Standard map
is a map on the two dimensional torus.


It belongs to a zoo
of Standard maps, maps of the form (x,y)>(f(x)y,x).


Twist maps
are discretisations of systems with
Hamiltonian = kinetic + potential energy.


Standard maps in
other contexts ,
like FrenkelKontorova, kicked Hamiltonians,
Fermi maps.



The relation
of the entropy with Lyapunov exponents
is given in Pesin theory.


Several
Methods
for estimating Lyapunov exponents are known.


One problem is the
coexistence
of stable and unstable behaviour in the phase space.


Tiny
little
ilands can be found arbitrarily deep inside the phase space.

