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... circles The bouquet of circles – the figure 8, in particular – has been studied as a motivating example to introduce the fundamental group on a graph (see p.189, [9]). More recently, Llibre and Todd =-=[8]-=-, for instance, studied a class of maps on a bouquet of circles from a dynamical system perspective. For 2 ≤ k1 ≤ k2 ≤ . . . ≤ kn, let Bn = (k1, k2, . . . , kn) be a bouquet of n ≥ 2 circles C1, C2, ....

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... ⌈n3 ⌉ if n ≥ 6. 2.2 Bouquet of Circles The bouquet of circles has been studied as a motivating example to introduce the fundamental group on a graph (see p.189, [23]). More recently, Llibre and Todd =-=[22]-=-, for instance, studied a class of maps on a bouquet of circles from a dynamical system perspective. It is well known that dim(Cn) = 2 for n ≥ 3. For kn ≥ kn−1 ≥ . . . ≥ k2 ≥ k1 ≥ 2, let Bn = (k1 + 1,...