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We study the dynamical properties of certain shift spaces. To help studythese properties we introduce two new classes of shifts, namely boundedlysupermultiplicative (BSM) shifts and balanced shifts. It turns out that anyalmost specified shift is both BSM and balanced, and any balanced shift is BSM.However, as we will demonstrate, there are examples of shifts which are BSM butnot balanced. We also study the measure theoretic properties of balancedshifts. We show that a shift space admits a Gibbs state if and only if it isbalanced.  Restricting ourselves to $S$-gap shifts, we relate certain dynamicalproperties of an $S$-gap shift to combinatorial properties from expansions innon-integer bases. This identification allows us to use the machinery fromexpansions in non-integer bases to give straightforward constructions of$S$-gap shifts with certain desirable properties. We show that for any$q\in(0,1)$ there is an $S$-gap shift which has the specification property andentropy $q$. We also use this identification to address the question, for agiven $q\in(0,1),$ how many $S$-gap shifts exist with entropy $q?$ For certainexceptional values of $q$ there is a unique $S$-gap shift with this entropy.

Dynamical properties of S-gap shifts and other shift spaces