Hutz, Normal Forms for Polynomial Dynamical Systems, ForALL Volume 1 Issue 1 (March 2023) 20-24.
Gauthier, Hutz, Kaschner, Symmetrization of rational maps: arithmetic properties and families of Lattes maps of Pk, Conformal Geometry and Dynamics 27 (2023), 98-117.
Benham, Galarraga, Hutz, Lupo, Peng, Towsley, New normal forms for degree three polynomials and rational functions. Involve, Vol. 16 (2023), No. 4, 605–620.
Benham, Galarraga, Hutz, Lupo, Peng, Towsley, Integrality and Thurston Rigidity for Bicritical PCF Polynomials. Periodica Mathematica Hungarica, Volume 87, pages 245–264, (2023).
Cai, Hutz, Mayer, Weinreich. Automorphism Groups of Endomorphisms of P^1(F_p), Glasgow Mathematics Journal, Volume 65, Issue 1, January 2023, 222 – 255.
Hutz, Patel, Periodic points and tail lengths of split polynomial maps modulo primes, Involve, Vol. 15 (2022), No. 2, 185–206.
Gontmacher, Hutz, Jorgenson, Srimani, Xu, Automorphism loci for degree 3 and degree 4 endomorphisms of the projective line, New York Journal of Mathematics Volume 27 (2021), 1613-1702.
Hutz, Multipliers and invariants of endomorphisms of projective space in dimension greater than 1, Journal of Number Theory of Bordeaux Vol. 32, No. 2 (2020), pp. 439-469.
Hutz, Stoll, Smallest representatives of SL(2,Z)-orbits of binary forms and endomorphisms of P^1, Acta Arith. 189, 283-308 (2019).
Hutz, Good reduction and canonical heights of subvarieties. Mathematical Research Letters, 25:6 (2018).
de Faria, Hutz, Automorphism groups and invariant theory on PN. Journal of Algebra and Its Applications, 17:9 (2018) 38 pages. doi.org/10.1142/S0219498818501621.
Benedetto, Faber, Hutz, Juul, Yasafuku, A large arboreal Galois representation for a cubic postcritically finite polynomial. Research in Number Theory 3:29 (2017). doi.org/10.1007/s40993-017-0092-8.
B. Hutz, Sage as a source for undergraduate research projects, PRIMUS (2016), 1–14. DOI: 10.1080/10511970.2016.1192072.
de Faria, Hutz, Combinatorics of cycle lengths on Wehler K3 surfaces over finite fields, New Zealand Journal of Mathematics 45 (2015), 19–31.
Hutz, Towsley, Thurston's theorem and Misiurewicz points for polynomial maps, New York Journal of Mathematics, 21 (2015), 297–319. Errata
Hutz, Determination of all rational preperiodic points for morphisms of PN, Mathematics of Computation, 84:291 (2015), 289–308. Errata
Hutz, Manes, The field of definition for dynamical systems on PN, Bulletin of the Institute of Mathematics Academia Sinica, 9:4 (2014), 585–601.
Hutz, Szpiro, Almost Newton, sometimes Lattès, Journal of Number Theory, 136 (2014), 423–437.
Hutz, Tepper, Multiplier spectra and the moduli space of degree 3 morphisms on P1, JP Journal of Algebra, Number Theory and Applications, 29:2 (2013), 189 – 206. Errata
Hutz, Ingram, On Poonen’s conjecture concerning rational preperiodic points of quadratic maps, Rocky Mountain Journal of Mathematics, 43:1 (2013), 193–204.
Benedetto, Ghioca, Hutz, Kurlberg, Scanlon, and Tucker, Periods of rational maps modulo primes, Mathematische Annalen, 355:2 (2013), 637–660.
Hutz, Effectivity of dynatomic cycles for morphisms of projective varieties using deformation theory, Proceedings of the AMS 140 (2012), 3507–3514.
Hutz, Hyde, Krause, Pre-images of quadratic dynamical systems, Involve 4:4 (2011), 343–363.
Faber, Hutz, Stoll, Pre-images of the origin: on the number of rational iterated pre-images of the origin under quadratic dynamical systems, International Journal of Number Theory 7:7 (2011), 1781–1806.
Hutz, Dynatomic cycles for morphisms of projective varieties, New York Journal of Mathematics, 16 (2010), 125–159.
Hutz, Rational periodic points for degree two polynomial maps on projective space, Acta Arithmetica 141(2010), 275–288.
Hutz, Finding Rational Periodic Points on Wehler K3 Surfaces, New Zealand Journal of Mathematics 39 (2009), 133–141.
Hutz, Good reduction of periodic points, Illinois Journal of Mathematics 53:4 (Winter 2009), 1109–1126. Errata
Faber, Hutz, Ingram, Jones, Manes, Tucker, Zieve, Uniform bounds on pre-images on quadratic dynamical systems. Mathematical Research Letters 16:1 (2009), 87–101.
Joint Mathematics Meetings Jan 8-10, 2025.
AMS Special Session on Mathematics Informed by Computing
“Using a Genetic Algorithm to Discover Extreme Examples in Arithmetic Dynamics”
American Institute of Mathematics. Dec 3-7, 2023
Open-source cyberinfrastructure supporting mathematics research
“A Database of Dynamical Systems”
I have contributed extensively to the open source computer algebra system SageMath.
You can find my open source projects on github
DynaBase - a database of dynamical system