Panraksa, Chatchawan; Samart, Detchat; Sriwongsa, Songpon A dynamical system proof of Niven’s theorem and its extensions. (English) Zbl 07802969 Bull. Aust. Math. Soc. 109, No. 1, 138-151 (2024). MSC: 37C25 11C08 11R04 33B10 PDFBibTeX XMLCite \textit{C. Panraksa} et al., Bull. Aust. Math. Soc. 109, No. 1, 138--151 (2024; Zbl 07802969) Full Text: DOI arXiv
Doyle, John R.; Faber, Xander New families satisfying the dynamical uniform boundedness principle over function fields. (English) Zbl 07796288 Math. Ann. 388, No. 1, 985-1000 (2024). MSC: 37P05 37P35 11R09 11G30 PDFBibTeX XMLCite \textit{J. R. Doyle} and \textit{X. Faber}, Math. Ann. 388, No. 1, 985--1000 (2024; Zbl 07796288) Full Text: DOI arXiv
Fu, Hang; Stoll, Michael Dynamics of quadratic polynomials and rational points on a curve of genus \(4\). (English) Zbl 07753434 Math. Comput. 93, No. 345, 397-410 (2024). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G30 11G40 14G05 14G10 14H45 37P05 PDFBibTeX XMLCite \textit{H. Fu} and \textit{M. Stoll}, Math. Comput. 93, No. 345, 397--410 (2024; Zbl 07753434) Full Text: DOI arXiv
Betts, L. Alexander Weight filtrations on Selmer schemes and the effective Chabauty-Kim method. (English) Zbl 1527.11056 Compos. Math. 159, No. 7, 1531-1605 (2023). MSC: 11G35 14F35 14G05 14G20 PDFBibTeX XMLCite \textit{L. A. Betts}, Compos. Math. 159, No. 7, 1531--1605 (2023; Zbl 1527.11056) Full Text: DOI arXiv
Hindes, Wade; Jacobs, Reiyah; Ye, Peter Irreducible polynomials in quadratic semigroups. (English) Zbl 1515.37109 J. Number Theory 248, 208-241 (2023). MSC: 37P15 11R09 37P05 PDFBibTeX XMLCite \textit{W. Hindes} et al., J. Number Theory 248, 208--241 (2023; Zbl 1515.37109) Full Text: DOI arXiv
Barsakçı, Burcu; Sadek, Mohammad Simultaneous rational periodic points of degree-2 rational maps. (English) Zbl 1505.37110 J. Number Theory 243, 715-728 (2023). MSC: 37P35 37P05 11G30 37P55 PDFBibTeX XMLCite \textit{B. Barsakçı} and \textit{M. Sadek}, J. Number Theory 243, 715--728 (2023; Zbl 1505.37110) Full Text: DOI arXiv
Demarco, Laura; Krieger, Holly; Ye, Hexi Common preperiodic points for quadratic polynomials. (English) Zbl 1503.37101 J. Mod. Dyn. 18, 363-413 (2022). MSC: 37P35 37F10 37P30 37P50 PDFBibTeX XMLCite \textit{L. Demarco} et al., J. Mod. Dyn. 18, 363--413 (2022; Zbl 1503.37101) Full Text: DOI arXiv
Eliahou, Shalom; Fares, Youssef Some results on the Flynn-Poonen-Schaefer conjecture. (English) Zbl 1505.37111 Can. Math. Bull. 65, No. 3, 598-611 (2022). Reviewer: Lajos Hajdu (Debrecen) MSC: 37P35 11C08 12E10 11S05 14G05 PDFBibTeX XMLCite \textit{S. Eliahou} and \textit{Y. Fares}, Can. Math. Bull. 65, No. 3, 598--611 (2022; Zbl 1505.37111) Full Text: DOI arXiv
Morton, Patrick; Raianu, Serban Arithmetic properties of 3-cycles of quadratic maps over \(\mathbb{Q}\). (English) Zbl 1521.11016 J. Number Theory 240, 685-729 (2022). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11C08 11R09 37P05 37P15 PDFBibTeX XMLCite \textit{P. Morton} and \textit{S. Raianu}, J. Number Theory 240, 685--729 (2022; Zbl 1521.11016) Full Text: DOI arXiv
Panraksa, Chatchawan Rational periodic points of \(x^d+c\) and Fermat-Catalan equations. (English) Zbl 1506.37121 Int. J. Number Theory 18, No. 5, 1111-1129 (2022). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 37P35 37P15 37P05 11C08 11D25 PDFBibTeX XMLCite \textit{C. Panraksa}, Int. J. Number Theory 18, No. 5, 1111--1129 (2022; Zbl 1506.37121) Full Text: DOI arXiv
Gontmacher, Brandon; Hutz, Benjamin; Jorgenson, Grayson; Srimani, Srinjoy; Xu, Simon Automorphism loci for degree 3 and degree 4 endomorphisms of the projective line. (English) Zbl 1491.37085 New York J. Math. 27, 1613-1702 (2021). MSC: 37P45 37P05 37P15 PDFBibTeX XMLCite \textit{B. Gontmacher} et al., New York J. Math. 27, 1613--1702 (2021; Zbl 1491.37085) Full Text: arXiv Link
Zhang, Robin A Galois-dynamics correspondence for unicritical polynomials. (English) Zbl 1485.37092 Arnold Math. J. 7, No. 3, 467-481 (2021). MSC: 37P05 37P35 11S15 12F10 PDFBibTeX XMLCite \textit{R. Zhang}, Arnold Math. J. 7, No. 3, 467--481 (2021; Zbl 1485.37092) Full Text: DOI arXiv
Sadek, Mohammad Families of polynomials of every degree with no rational preperiodic points. (Familles de polynômes de degré arbitraire sans points prépériodiques rationnels.) (English. French summary) Zbl 1462.37111 C. R., Math., Acad. Sci. Paris 359, No. 2, 195-197 (2021). MSC: 37P35 37P05 PDFBibTeX XMLCite \textit{M. Sadek}, C. R., Math., Acad. Sci. Paris 359, No. 2, 195--197 (2021; Zbl 1462.37111) Full Text: DOI arXiv
Huang, Keping Uniform bounds for periods of endomorphisms of varieties. (English) Zbl 1472.11197 J. Number Theory 221, 358-364 (2021). Reviewer: Rubén A. Hidalgo (Temuco) MSC: 11G30 37P05 14G40 PDFBibTeX XMLCite \textit{K. Huang}, J. Number Theory 221, 358--364 (2021; Zbl 1472.11197) Full Text: DOI arXiv
Krumm, David; Sutherland, Nicole Galois groups over rational function fields and explicit Hilbert irreducibility. (English) Zbl 1461.11152 J. Symb. Comput. 103, 108-126 (2021). MSC: 11R32 11R09 12F10 11Y40 PDFBibTeX XMLCite \textit{D. Krumm} and \textit{N. Sutherland}, J. Symb. Comput. 103, 108--126 (2021; Zbl 1461.11152) Full Text: DOI arXiv
Doyle, John R. Preperiodic points for quadratic polynomials over cyclotomic quadratic fields. (English) Zbl 1465.37111 Acta Arith. 196, No. 3, 219-268 (2020). Reviewer: Nikolai L. Manev (Sofia) MSC: 37P35 37P05 37P15 14G05 11R18 PDFBibTeX XMLCite \textit{J. R. Doyle}, Acta Arith. 196, No. 3, 219--268 (2020; Zbl 1465.37111) Full Text: DOI arXiv
Doyle, John R.; Silverman, Joseph H. Moduli spaces for dynamical systems with portraits. (English) Zbl 1448.37132 Ill. J. Math. 64, No. 3, 375-465 (2020). MSC: 37P45 37P15 PDFBibTeX XMLCite \textit{J. R. Doyle} and \textit{J. H. Silverman}, Ill. J. Math. 64, No. 3, 375--465 (2020; Zbl 1448.37132) Full Text: DOI arXiv Euclid
Ingram, Patrick Canonical heights and preperiodic points for certain weighted homogeneous families of polynomials. (English) Zbl 1456.37108 Int. Math. Res. Not. 2019, No. 15, 4859-4879 (2019). MSC: 37P05 37P30 11G50 PDFBibTeX XMLCite \textit{P. Ingram}, Int. Math. Res. Not. 2019, No. 15, 4859--4879 (2019; Zbl 1456.37108) Full Text: DOI arXiv
Vishkautsan, Solomon Quadratic rational functions with a rational periodic critical point of period 3. (English. French summary) Zbl 1451.37118 J. Théor. Nombres Bordx. 31, No. 1, 49-79 (2019). MSC: 37P05 37P35 PDFBibTeX XMLCite \textit{S. Vishkautsan}, J. Théor. Nombres Bordx. 31, No. 1, 49--79 (2019; Zbl 1451.37118) Full Text: DOI arXiv
Benedetto, Robert; Ingram, Patrick; Jones, Rafe; Manes, Michelle; Silverman, Joseph H.; Tucker, Thomas J. Current trends and open problems in arithmetic dynamics. (English) Zbl 1468.37001 Bull. Am. Math. Soc., New Ser. 56, No. 4, 611-685 (2019). Reviewer: Lingmin Liao (Créteil) MSC: 37-02 37Pxx PDFBibTeX XMLCite \textit{R. Benedetto} et al., Bull. Am. Math. Soc., New Ser. 56, No. 4, 611--685 (2019; Zbl 1468.37001) Full Text: DOI arXiv
Canci, Jung Kyu; Troncoso, Sebastian; Vishkautsan, Solomon Scarcity of finite orbits for rational functions over a number field. (English) Zbl 1431.37075 Acta Arith. 190, No. 3, 221-237 (2019). Reviewer: Mahadi Ddamulira (Graz) MSC: 37P05 37P35 11D45 PDFBibTeX XMLCite \textit{J. K. Canci} et al., Acta Arith. 190, No. 3, 221--237 (2019; Zbl 1431.37075) Full Text: DOI arXiv
Hindes, Wade Finite orbit points for sets of quadratic polynomials. (English) Zbl 1435.37110 Int. J. Number Theory 15, No. 8, 1693-1719 (2019). Reviewer: Roberto Dvornicich (Pisa) MSC: 37P55 11G50 37P05 37P35 37P30 PDFBibTeX XMLCite \textit{W. Hindes}, Int. J. Number Theory 15, No. 8, 1693--1719 (2019; Zbl 1435.37110) Full Text: DOI arXiv
Krumm, David A finiteness theorem for specializations of dynatomic polynomials. (English) Zbl 1442.37121 Algebra Number Theory 13, No. 4, 963-993 (2019). MSC: 37P05 37P35 11S15 PDFBibTeX XMLCite \textit{D. Krumm}, Algebra Number Theory 13, No. 4, 963--993 (2019; Zbl 1442.37121) Full Text: DOI arXiv
Doyle, John R. Dynamical modular curves for quadratic polynomial maps. (English) Zbl 1427.37071 Trans. Am. Math. Soc. 371, No. 8, 5655-5685 (2019). Reviewer: Gabriel D. Villa Salvador (México D. F.) MSC: 37P05 37P45 11R58 14H05 PDFBibTeX XMLCite \textit{J. R. Doyle}, Trans. Am. Math. Soc. 371, No. 8, 5655--5685 (2019; Zbl 1427.37071) Full Text: DOI arXiv
Doyle, John R. Preperiodic points for quadratic polynomials with small cycles over quadratic fields. (English) Zbl 1400.37109 Math. Z. 289, No. 1-2, 729-786 (2018). Reviewer: Franco Vivaldi (London) MSC: 37P05 37P35 PDFBibTeX XMLCite \textit{J. R. Doyle}, Math. Z. 289, No. 1--2, 729--786 (2018; Zbl 1400.37109) Full Text: DOI arXiv
Krumm, David Galois groups in a family of dynatomic polynomials. (English) Zbl 1489.11189 J. Number Theory 187, 469-511 (2018). MSC: 11R32 11R09 PDFBibTeX XMLCite \textit{D. Krumm}, J. Number Theory 187, 469--511 (2018; Zbl 1489.11189) Full Text: DOI arXiv
Troncoso, Sebastian Bounds for preperiodic points for maps with good reduction. (English) Zbl 1406.37070 J. Number Theory 181, 51-72 (2017). MSC: 37P05 11D45 PDFBibTeX XMLCite \textit{S. Troncoso}, J. Number Theory 181, 51--72 (2017; Zbl 1406.37070) Full Text: DOI arXiv
Canci, Jung Kyu; Vishkautsan, Solomon Quadratic maps with a periodic critical point of period 2. (English) Zbl 1392.37100 Int. J. Number Theory 13, No. 6, 1393-1417 (2017). MSC: 37P05 37P35 PDFBibTeX XMLCite \textit{J. K. Canci} and \textit{S. Vishkautsan}, Int. J. Number Theory 13, No. 6, 1393--1417 (2017; Zbl 1392.37100) Full Text: DOI arXiv
Pasten, Hector; Vidaux, Xavier Positive existential definability of multiplication from addition and the range of a polynomial. (English) Zbl 1408.11116 Isr. J. Math. 216, No. 1, 273-306 (2016). MSC: 11U05 03C40 13F20 PDFBibTeX XMLCite \textit{H. Pasten} and \textit{X. Vidaux}, Isr. J. Math. 216, No. 1, 273--306 (2016; Zbl 1408.11116) Full Text: DOI
Konyagin, Sergei V.; Luca, Florian; Mans, Bernard; Mathieson, Luke; Sha, Min; Shparlinski, Igor E. Functional graphs of polynomials over finite fields. (English) Zbl 1327.05323 J. Comb. Theory, Ser. B 116, 87-122 (2016). MSC: 05C85 05C05 05C20 PDFBibTeX XMLCite \textit{S. V. Konyagin} et al., J. Comb. Theory, Ser. B 116, 87--122 (2016; Zbl 1327.05323) Full Text: DOI arXiv
Doyle, John R.; Krumm, David Computing algebraic numbers of bounded height. (English) Zbl 1330.11081 Math. Comput. 84, No. 296, 2867-2891 (2015). MSC: 11Y40 PDFBibTeX XMLCite \textit{J. R. Doyle} and \textit{D. Krumm}, Math. Comput. 84, No. 296, 2867--2891 (2015; Zbl 1330.11081) Full Text: DOI arXiv
Hindes, Wade The arithmetic of curves defined by iteration. (English) Zbl 1330.14032 Acta Arith. 169, No. 1, 1-27 (2015). Reviewer: Yu Yasufuku (Tokyo) MSC: 14G05 37P05 12F10 37P15 11G30 11G05 14H45 20E08 37P55 14H25 PDFBibTeX XMLCite \textit{W. Hindes}, Acta Arith. 169, No. 1, 1--27 (2015; Zbl 1330.14032) Full Text: DOI arXiv
Faber, Xander Benedetto’s trick and existence of rational preperiodic structures for quadratic polynomials. (English) Zbl 1392.37116 Proc. Am. Math. Soc. 143, No. 2, 685-694 (2015). MSC: 37P35 37P05 37P40 14E05 PDFBibTeX XMLCite \textit{X. Faber}, Proc. Am. Math. Soc. 143, No. 2, 685--694 (2015; Zbl 1392.37116) Full Text: DOI arXiv
Hutz, Benjamin Determination of all rational preperiodic points for morphisms of PN. (English) Zbl 1392.37104 Math. Comput. 84, No. 291, 289-308 (2015). MSC: 37P05 37P15 37P45 PDFBibTeX XMLCite \textit{B. Hutz}, Math. Comput. 84, No. 291, 289--308 (2015; Zbl 1392.37104) Full Text: DOI arXiv
Faber, Xander; Manes, Michelle; Viray, Bianca Computing conjugating sets and automorphism groups of rational functions. (English) Zbl 1391.37066 J. Algebra 423, 1161-1190 (2015). MSC: 37P05 11Y16 PDFBibTeX XMLCite \textit{X. Faber} et al., J. Algebra 423, 1161--1190 (2015; Zbl 1391.37066) Full Text: DOI arXiv
Benedetto, Robert L.; Chen, Ruqian; Hyde, Trevor; Kovacheva, Yordanka; White, Colin Small dynamical heights for quadratic polynomials and rational functions. (English) Zbl 1347.37158 Exp. Math. 23, No. 4, 433-447 (2014). MSC: 37P35 37P30 11G50 37P05 PDFBibTeX XMLCite \textit{R. L. Benedetto} et al., Exp. Math. 23, No. 4, 433--447 (2014; Zbl 1347.37158) Full Text: DOI arXiv
Levy, Alon; Manes, Michelle; Thompson, Bianca Uniform bounds for preperiodic points in families of twists. (English) Zbl 1401.37101 Proc. Am. Math. Soc. 142, No. 9, 3075-3088 (2014). Reviewer: Xiao Xiao (Utica) MSC: 37P05 11R99 PDFBibTeX XMLCite \textit{A. Levy} et al., Proc. Am. Math. Soc. 142, No. 9, 3075--3088 (2014; Zbl 1401.37101) Full Text: DOI arXiv
Lukas, David; Manes, Michelle; Yap, Diane A census of quadratic post-critically finite rational functions defined over \(\mathbb{Q}\). (English) Zbl 1369.37091 LMS J. Comput. Math. 17A, Spec. Iss., 314-329 (2014). MSC: 37P05 37P15 PDFBibTeX XMLCite \textit{D. Lukas} et al., LMS J. Comput. Math. 17A, 314--329 (2014; Zbl 1369.37091) Full Text: DOI arXiv
Hutz, Benjamin; Ingram, Patrick On Poonen’s conjecture concerning rational preperiodic points of quadratic maps. (English) Zbl 1316.37042 Rocky Mt. J. Math. 43, No. 1, 193-204 (2013). Reviewer: Yu Yasufuku (Tokyo) MSC: 37P05 37P35 PDFBibTeX XMLCite \textit{B. Hutz} and \textit{P. Ingram}, Rocky Mt. J. Math. 43, No. 1, 193--204 (2013; Zbl 1316.37042) Full Text: DOI arXiv Euclid
Faber, Xander; Hutz, Benjamin; Stoll, Michael On the number of rational iterated preimages of the origin under quadratic dynamical systems. (English) Zbl 1242.14019 Int. J. Number Theory 7, No. 7, 1781-1806 (2011). Reviewer: Min Ho Lee (Cedar Falls) MSC: 14G05 11G18 11Y50 37F10 PDFBibTeX XMLCite \textit{X. Faber} et al., Int. J. Number Theory 7, No. 7, 1781--1806 (2011; Zbl 1242.14019) Full Text: DOI arXiv
Benedetto, Robert L. Book review of: Joseph H. Silverman, The arithmetic of dynamical systems. (English) Zbl 1292.00012 Bull. Am. Math. Soc., New Ser. 46, No. 1, 157-164 (2009). MSC: 00A17 37-01 11-01 37F10 37C25 11G50 11G05 11G07 PDFBibTeX XMLCite \textit{R. L. Benedetto}, Bull. Am. Math. Soc., New Ser. 46, No. 1, 157--164 (2009; Zbl 1292.00012) Full Text: DOI
Ingram, Patrick Lower bounds on the canonical height associated to the morphism \(\phi(z)= z^d+c\). (English) Zbl 1239.11071 Monatsh. Math. 157, No. 1, 69-89 (2009). Reviewer: Thomas J. Tucker (Rochester) MSC: 11G50 37F10 11G99 PDFBibTeX XMLCite \textit{P. Ingram}, Monatsh. Math. 157, No. 1, 69--89 (2009; Zbl 1239.11071) Full Text: DOI arXiv
Stoll, Michael Rational 6-cycles under iteration of quadratic polynomials. (English) Zbl 1222.11083 LMS J. Comput. Math. 11, 367-380 (2008). MSC: 11G30 11G40 37P05 37P35 PDFBibTeX XMLCite \textit{M. Stoll}, LMS J. Comput. Math. 11, 367--380 (2008; Zbl 1222.11083) Full Text: DOI arXiv
Benedetto, Robert L. Preperiodic points of polynomials over global fields. (English) Zbl 1156.37009 J. Reine Angew. Math. 608, 123-153 (2007). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 37P20 37P15 37P35 11C08 11R09 11R58 14E05 37F50 PDFBibTeX XMLCite \textit{R. L. Benedetto}, J. Reine Angew. Math. 608, 123--153 (2007; Zbl 1156.37009) Full Text: DOI arXiv
Bruin, N.; Győry, K.; Hajdu, L.; Tengely, Sz. Arithmetic progressions consisting of unlike powers. (English) Zbl 1142.11018 Indag. Math., New Ser. 17, No. 4, 539-555 (2006). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11D41 11B25 11G30 11Y50 PDFBibTeX XMLCite \textit{N. Bruin} et al., Indag. Math., New Ser. 17, No. 4, 539--555 (2006; Zbl 1142.11018) Full Text: DOI arXiv
Marszałek, Roman; Narkiewicz, Władyslaw Finite polynomial orbits in quadratic rings. (English) Zbl 1122.11069 Ramanujan J. 12, No. 1, 91-130 (2006). Reviewer: Franco Vivaldi (London) MSC: 11R09 11R11 37F10 PDFBibTeX XMLCite \textit{R. Marszałek} and \textit{W. Narkiewicz}, Ramanujan J. 12, No. 1, 91--130 (2006; Zbl 1122.11069) Full Text: DOI