Linearized transverse equation for a surface thermostat
= Linearized transverse equation for a surface thermostat
{title2=$\dot y=z,\qquad\dot z=-(K-H\lambda+\lambda^2)y+(V\lambda)z$}
Write a tangent variation of a <surface thermostat> as $aF+yH+zV$ in the canonical frame. The commutators $[F,H]=-\lambda F+(K-H\lambda+\lambda^2)V$ and $[F,V]=-H-(V\lambda)V$ give $\dot a=\lambda y$ and the stated transverse equation. Near the vertical projective direction, $r=y/z$ obeys $\dot r=1-(V\lambda)r+(K-H\lambda+\lambda^2)r^2$.