… theoretical results stating that inductive sets are unique with respect to (wrt) invariant sets. …
We say the invariant sets of a system are closed under substitution 3 or substitution closed, for …

… Then any invariant set Z is characterized as Z=F+(K) for some set K of ascendable elements…
if F is a substitution over a finite alphabet, then for any invariant set Z there exists a set S of …

… substitution tilings. Under some hypotheses, we show that the dynamics of the substitution
… This approach also allows computation of the zeta function for the substitution. We discuss C…

… OVer a finite set (or the set of a11 Words over an a1phabet) and F is a substitution On it ,then
for any ascendable e1ement xe X there does exist a repeatable point Z such that xe F"(z) (Lemma�…

… invariant sets are unstable in this case 5 ) or becomes sign-definite in the manifold (4.3) (the
invariant sets … of γ 3 0 ( t ) and k and substituting the resulting expressions into equality (4.4), …

In this paper, we examine the ergodic properties of a bisequence over some finite set of symbols
which is generated by a substitution. By a substitution, we mean a mapping which maps …

… topological invariant (in terms to be described shortly) for the one-dimensional substitution
… We will also derive, and apply, a numerical invariant of weak equivalence of substitutions …

… In particular we show that an ordered invariant set and the corresponding exact … invariant
set for the KdV equation. Let us find a linear solution F{u) = Си of the ODE (2.1). Substituting we …

… sub-universes, and the behavior of transpositionally invariant set classes in the larger mod-12
… leads me to propose a set of homomorphic mappings of pc sets based on membership of …

… Then we discuss invariants, dene a substitution system based on an algebraic high-level …
invariants arise as solutions to a set of equations on the arrows in this category of invariants. …