### Table 1: Bifurcation Points for the H enon map Bifurcation

1999

"... In PAGE 23: ... Representative phase portraits are also shown. See Table1 for bifurcation values. The second twist 1 can be used in two di erent ways.... ..."

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### Table 2: Bifurcation in dependence to neness

"... In PAGE 11: ... In this cases one obtaines a unique numerical branch f( h(r); r); fh( h(r); r) = 0; r 2 [?2; 2]g: Numerical bifurcation is reported for RL 4. The corresponding bifurcation intervals are presented in Table2 . The ALCON2 program computes three solution branches ( 1(r); r); ( 2(r); r); ( 3(r); r) such that fh( i(r); r) = 0 i = 1; 2; 3 (r0 lt; r lt; r1): In order to decide whether these three branches represent stable or unstable discrete minimal surfaces the eigenvalues of some nite-di erence approximation D fh( i(r); r) (i = 1; 2; 3) of Dfh at some parameter values r 2 (r0; r1) are computed.... ..."

### Table 1: Bifurcation Points for the H enon map Bifurcation

1999

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### TABLE II EIGENVALUES AT HOPF BIFURCATION

### Table 5: Bifurcation in dependence to neness, n=18

"... In PAGE 17: ... 24, 25). Table5 shows the bifurcation intervals corresponding the the di erent re nement levels.... ..."

### Table 6: Homoclinic bifurcations bounding the gaps

1999

"... In PAGE 35: ... Our numerical evidence, which extends their study by an order of magnitude, supports this conjecture. Upon examining the orbits that limit on the endpoints of the gap up to period 24, we can extrapolate and nd that each of the ve largest gaps is bounded by a homoclinic bifurcation, see Table6 . Thus we see that... In PAGE 38: ... First, we studied an order of magnitude more orbits than the original experiment and yet the gaps originally reported by DMS persisted. We observed that homoclinic bifurcations are responsible for these gaps and we listed the symbolic labels of the orbits that form the gap endpoints in Table6 . These gaps correspond to the creation and destruction of parame- ter intervals where the dynamics of the area-preserving H enon map appears... ..."

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### Table 1. Parameters for periodic behaviour and bifurcation.

"... In PAGE 14: ... The left hand diagram shows the four coset orbits for H4 and the right hand diagram shows a close up of one of these, decomposed as the union of 25 coset orbits for H100. This suggests that there may be an elliptic periodic point P = P1, of order 4, with orbit fP1; P2; P3; P4g, such that there exist neighbourhoods N(P1); N(P2); N(P3); N(P4) with orb((0; 0)) S 1 i 4 N(Pi) and H(N(Pi)) N(Pi+1mod4): Values of the parameters at which we have observed similar behaviour, presumably in uenced by elliptic periodic points, are shown on the left of Table1 . The \islands quot; of the set B corresponding to these may be identi ed using the applet and entering r and .... ..."

### Table 4. (a) Score values of bifurcation

2002

### Table 1 Technology bifurcation in the 2003 ITRS roadmap.

### TABLE 2 Definitions and examples of codimension-one and -two bifurcations Codimension-one bifurcations

2006

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