# Dynabase (https://dynabase.org): Summary of Extreme Examples, postcritically finite maps (all of them, for each row), polynomial maps over QQ # # Load in Sage with load(""). It defines dynabase_systems, a list of # [map, label] pairs in table order: the map as a DynamicalSystem over the field of # its table row, and its Dynabase label (dimension.sigma1.sigma2.ordinal). # Loading also (re)defines K, P, x, y. dynabase_systems = [] K = QQ P. = ProjectiveSpace(K, 1) # Poonen1998, Ingram2012, Doyle2014, Lukas2014, CV2017, Doyle2018, Doyle2020, DoHi2025 dynabase_systems.append([DynamicalSystem([x^2 - y^2, y^2], domain=P), '1.b5876aa4.6951d87f.1']) # Morton1992, FN1997, Poonen1998, Manes2008, Ingram2012, Doyle2014, Lukas2014, Doyle2018, Doyle2020 dynabase_systems.append([DynamicalSystem([x^2, y^2], domain=P), '1.a68cf1ff.024ac6d7.1']) # WR1994, Poonen1998, Ingram2012, Doyle2014, Lukas2014, Doyle2018, Doyle2020 dynabase_systems.append([DynamicalSystem([x^2 - 2*y^2, y^2], domain=P), '1.a6935bbd.880302df.1']) # Benedetto2009, AMT2020 dynabase_systems.append([DynamicalSystem([x^3 - y^3, -y^3], domain=P), '1.7e36c441.20e2ac14.1']) # Benedetto2009, AMT2020 dynabase_systems.append([DynamicalSystem([x^3 - 3*x*y^2 + 2*y^3, 2*y^3], domain=P), '1.5ac401c2.34c3c88c.1']) # Benedetto2009, AMT2020 dynabase_systems.append([DynamicalSystem([x^3 - 3*x*y^2 - 2*y^3, -2*y^3], domain=P), '1.5b621046.0e8d94e9.1']) # Benedetto2009, AMT2020 dynabase_systems.append([DynamicalSystem([3*x^3 - 9*x*y^2 + 2*y^3, 4*y^3], domain=P), '1.6502de33.969c7b25.1']) # Benedetto2009, Ingram2012, AMT2020 dynabase_systems.append([DynamicalSystem([x^3 - 3/4*x*y^2 + 3/4*y^3, y^3], domain=P), '1.9fcfd25c.91fd0195.1']) # Benedetto2009, AMT2020 dynabase_systems.append([DynamicalSystem([x^3 + 3*x^2*y - 4*y^3, -4*y^3], domain=P), '1.194ce1a9.8660b31e.1']) # Benedetto2009, AMT2020 dynabase_systems.append([DynamicalSystem([x^3 - 3*x*y^2, -y^3], domain=P), '1.e8bb745c.fe98c06c.1']) # FN1997, Ingram2012, AMT2020 dynabase_systems.append([DynamicalSystem([x^3, y^3], domain=P), '1.5fe37194.3d72adff.1']) # AMT2020 dynabase_systems.append([DynamicalSystem([x^3 + 3*x^2*y, 3*x*y^2 + y^3], domain=P), '1.ad8ccd97.61cd033e.1']) # AMT2020 dynabase_systems.append([DynamicalSystem([2*x^3 - 3*x^2*y + 2*y^3, -2*y^3], domain=P), '1.3e20f681.046df03c.1']) # AMT2020 dynabase_systems.append([DynamicalSystem([2*x^3 + 3*x^2*y - y^3, y^3], domain=P), '1.354addff.61cd033e.1']) # AMT2020 dynabase_systems.append([DynamicalSystem([3*x^3, -2*x^3 + 6*x^2*y + 3*x*y^2 - 4*y^3], domain=P), '1.b40fd63f.4b09c087.1']) # Ingram2012, AMT2020 dynabase_systems.append([DynamicalSystem([x^3 - 3*x*y^2, y^3], domain=P), '1.4b199b71.fe98c06c.1']) # AMT2020 dynabase_systems.append([DynamicalSystem([2*x^3 - 3*x*y^2 - 2*y^3, -2*y^3], domain=P), '1.31ca8b83.56a37501.1']) # AMT2020 dynabase_systems.append([DynamicalSystem([4*x^3 + 3*x^2*y + 6*x*y^2 - 3*y^3, -7*y^3], domain=P), '1.170955e6.895e6900.1']) # Ingram2012 dynabase_systems.append([DynamicalSystem([x^3 - 3/2*x*y^2, y^3], domain=P), '1.354addff.61cd033e.2']) # Ingram2012 dynabase_systems.append([DynamicalSystem([x^3 + 3/2*x*y^2, y^3], domain=P), '1.ad8ccd97.61cd033e.2']) # Ingram2012 dynabase_systems.append([DynamicalSystem([x^3 + 3*x*y^2, y^3], domain=P), '1.e8bb745c.fe98c06c.2']) # FN1997, GHJSX2021, Fraser2024 dynabase_systems.append([DynamicalSystem([x^4, y^4], domain=P), '1.024ac6d7.76c4de71.1']) # Fraser2024 dynabase_systems.append([DynamicalSystem([x^4 - y^4, y^4], domain=P), '1.770c2622.7cef54b3.1']) # Fraser2024 dynabase_systems.append([DynamicalSystem([2*x^4 - y^4, -y^4], domain=P), '1.5457b5e3.e9909514.1']) # Fraser2024 dynabase_systems.append([DynamicalSystem([x^4, 4*x*y^3 + 3*y^4], domain=P), '1.d445c2f7.72c00a36.1']) # Fraser2024 dynabase_systems.append([DynamicalSystem([3*x^4 - 4*x^3*y + y^4, y^4], domain=P), '1.a48ef78e.703b5deb.1']) # Fraser2024 dynabase_systems.append([DynamicalSystem([x^4 - 2/3*x^2*y^2 - 8/27*x*y^3 + 26/27*y^4, y^4], domain=P), '1.8af865e4.2d8ff491.1']) # Fraser2024 dynabase_systems.append([DynamicalSystem([x^4 - 2/3*x^2*y^2 + 8/27*x*y^3 - 19/27*y^4, y^4], domain=P), '1.9da62374.0f726d75.1']) # Fraser2024 dynabase_systems.append([DynamicalSystem([3*x^4 + 4*x^3*y - 6*x^2*y^2 - 12*x*y^3 + 5*y^4, 6*y^4], domain=P), '1.a70750b0.c07be85c.1']) # Fraser2024 dynabase_systems.append([DynamicalSystem([3*x^4 - 8*x^3*y, -6*y^4], domain=P), '1.da89c05a.4e01541d.1']) # Fraser2024 dynabase_systems.append([DynamicalSystem([x^4 - 2*x^2*y^2 + y^4, y^4], domain=P), '1.770c2622.7cef54b3.2']) # Fraser2024 dynabase_systems.append([DynamicalSystem([2*x^4 - 4*x^2*y^2 + y^4, y^4], domain=P), '1.e029f05a.0d52105e.1']) # Fraser2024 dynabase_systems.append([DynamicalSystem([x^4 - 2*x^2*y^2, y^4], domain=P), '1.6951d87f.f9bbe0ed.1']) # Fraser2024 dynabase_systems.append([DynamicalSystem([x^4 + 4*x*y^3, 3*y^4], domain=P), '1.8e57877c.24b4743f.1']) # Fraser2024 dynabase_systems.append([DynamicalSystem([x^4 - 4*x^2*y^2, 2*y^4], domain=P), '1.e029f05a.0d52105e.2']) # Fraser2024 dynabase_systems.append([DynamicalSystem([x^4 - 4*x^2*y^2 + 4*y^4, 2*y^4], domain=P), '1.5457b5e3.e9909514.2']) # Fraser2024 dynabase_systems.append([DynamicalSystem([x^4 - 4*x^2*y^2 + 2*y^4, y^4], domain=P), '1.880302df.903704ba.1']) # FN1997 dynabase_systems.append([DynamicalSystem([x^5, y^5], domain=P), '1.6f752b35.d8e415c3.1']) # FN1997 dynabase_systems.append([DynamicalSystem([x^6, y^6], domain=P), '1.d60c7e5d.aa38682f.1']) # FN1997 dynabase_systems.append([DynamicalSystem([x^7, y^7], domain=P), '1.6c5154c1.84c0eaef.1']) # FN1997 dynabase_systems.append([DynamicalSystem([x^8, y^8], domain=P), '1.a2cb972c.bc5e6238.1']) # FN1997 dynabase_systems.append([DynamicalSystem([x^9, y^9], domain=P), '1.3d72adff.f501313b.1']) # FN1997 dynabase_systems.append([DynamicalSystem([x^10, y^10], domain=P), '1.f0bbe529.7d4a3a0d.1']) print("Dynabase: 43 dynamical systems in dynabase_systems")