(* Code for calculating the zeta function for the pinball *)
Get["orbits.m"]
t[n_] := Exp[s Tp[n]] z^np[n]/Abs[lam[n]]
zeta = Series[Product[(1-t[i]), {i,0,40}], {z,0,7}]
gamma[m_] := Block[{zeta1},
	  zeta1 = Normal[Series[zeta, {z,0,m}]] /.z->1;
	  N[s /. FindRoot[zeta1==0, {s, 0.4}], 16]
	]
gam = Table[gamma[i], {i,1,7}]
Print["Escape rate = ", gam]
zeta1 = zeta /. s -> gamma[7]
Plot[Evaluate[Normal[zeta1]], {z, -100, 100}]
ListPlot[Log[Abs[CoefficientList[zeta1, z]]]]