= Hyperbolic component
In the <quadratic polynomial> family $f_c(z)=z^2+c$, a <hyperbolic component> is a <connected component> of the set of parameters for which $f_c$ has an <attracting periodic point>. The finite <critical orbit> is then attracted to that cycle. Its exact period is constant throughout the component. The component is open because an <attracting periodic point> and its strict multiplier inequality persist under small parameter changes.
The <main cardioid> has an <attracting periodic point> of period one; the <period-two bulb> has an attracting exact two-cycle. Their <periodic-orbit multipliers> give the explicit coordinates $c=\lambda/2-\lambda^2/4$ and $\lambda=4(c+1)$, respectively, with $|\lambda|<1$. More generally the attracting-cycle multiplier gives a conformal coordinate on each <quadratic polynomial> <hyperbolic component>.
This is a definition within the specified parameter family. For general <rational maps>, the existence of one attracting cycle alone does not require every <critical orbit> to approach an attracting cycle, so it does not by itself establish global hyperbolicity.<Dynamics in one complex variable: introductory lectures by John Milnor>[Appendix F, quadratic parameter space and attracting-cycle components]{ref}
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