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The Chirikov Standard map
is a map on the two dimensional torus.
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It belongs to a zoo
of Standard maps, maps of the form (x,y)->(f(x)-y,x).
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Twist maps
are discretisations of systems with
Hamiltonian = kinetic + potential energy.
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Standard maps in
other contexts ,
like Frenkel-Kontorova, kicked Hamiltonians,
Fermi maps.
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The relation
of the entropy with Lyapunov exponents
is given in Pesin theory.
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Several
Methods
for estimating Lyapunov exponents are known.
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One problem is the
coexistence
of stable and unstable behaviour in the phase space.
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Tiny
little
ilands can be found arbitrarily deep inside the phase space.
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