Monodromy Automorphism 001x100 by Karl Papadantonakis and Jodn Hubbard

The first loop whose associated monodromy automorphism is convincing.

This loop, to depth 10, appears to give the automorphism 001x100. It exists in the slice c=-3.5, and DOES NOT appear to exist in the slice c=-3, where some other bifurcation (the 101x1 bifurcation) appears to have collided with the tip of this one.

pictoral representation of the automorphism:

The following tables give the permutation on the critical points down to depth 10; the labelling is by itinerary.

Level 5
0.11100     0.10100      *
0.10100     0.11100      *

Level 6
0.011100    0.010100     *
0.010100    0.011100     *
0.111001    0.101001     *
0.111000    0.101000     *
0.101000    0.111000     *
0.101001    0.111001     *

Level 7
0.0011100   0.0010100    *
0.0010100   0.0011100    *
0.0111001   0.0101001    *
0.0111000   0.0101000    *
0.0101000   0.0111000    *
0.0101001   0.0111001    *
0.1110010   0.1010010    *
0.1110011   0.1010011    *
0.1110001   0.1010001    *
0.1110000   0.1010000    *
0.1010000   0.1110000    *
0.1010001   0.1110001    *
0.1010011   0.1110011    *
0.1010010   0.1110010    *

Level 8
0.00011100  0.00010100   *
0.00010100  0.00011100   *
0.00111001  0.00101001   *
0.00111000  0.00101000   *
0.00101000  0.00111000   *
0.00101001  0.00111001   *
0.01110010  0.01010010   *
0.01110011  0.01010011   *
0.01110001  0.01010001   *
0.01110000  0.01010000   *
0.01010000  0.01110000   *
0.01010001  0.01110001   *
0.01010011  0.01110011   *
0.01010010  0.01110010   *
0.11100100  0.10100100   *
0.11100101  0.10100101   *
0.11100111  0.10100111   *
0.11100110  0.10100110   *
0.11100010  0.10100010   *
0.11100011  0.10100011   *
0.11100001  0.10100001   *
0.11100000  0.10100000   *
0.10100000  0.11100000   *
0.10100001  0.11100001   *
0.10100011  0.11100011   *
0.10100010  0.11100010   *
0.10100110  0.11100110   *
0.10100111  0.11100111   *
0.10100101  0.11100101   *
0.10100100  0.11100100   *
0.10010100  0.10011100   *
0.10011100  0.10010100   *


Levels 9 and 10 (with annotation)

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