Arithmetic dynamics (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Arithmetic dynamics" in English language version.

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12ams.org

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ams.org

mathscinet.ams.org

Silverman, Joseph H. (2007). The Arithmetic of Dynamical Systems. Graduate Texts in Mathematics. Vol. 241. New York: Springer. doi:10.1007/978-0-387-69904-2. ISBN 978-0-387-69903-5. MR 2316407.
Northcott, Douglas Geoffrey (1950). "Periodic points on an algebraic variety". Annals of Mathematics. 51 (1): 167–177. doi:10.2307/1969504. JSTOR 1969504. MR 0034607.
Morton, Patrick; Silverman, Joseph H. (1994). "Rational periodic points of rational functions". International Mathematics Research Notices. 1994 (2): 97–110. doi:10.1155/S1073792894000127. MR 1264933.
Morton, Patrick (1992). "Arithmetic properties of periodic points of quadratic maps". Acta Arithmetica. 62 (4): 343–372. doi:10.4064/aa-62-4-343-372. MR 1199627.
Flynn, Eugene V.; Poonen, Bjorn; Schaefer, Edward F. (1997). "Cycles of quadratic polynomials and rational points on a genus-2 curve". Duke Mathematical Journal. 90 (3): 435–463. arXiv:math/9508211. doi:10.1215/S0012-7094-97-09011-6. MR 1480542. S2CID 15169450.
Stoll, Michael (2008). "Rational 6-cycles under iteration of quadratic polynomials". LMS Journal of Computation and Mathematics. 11: 367–380. arXiv:0803.2836. Bibcode:2008arXiv0803.2836S. doi:10.1112/S1461157000000644. MR 2465796. S2CID 14082110.
Poonen, Bjorn (1998). "The classification of rational preperiodic points of quadratic polynomials over $Q$ : a refined conjecture". Mathematische Zeitschrift. 228 (1): 11–29. doi:10.1007/PL00004405. MR 1617987. S2CID 118160396.
Silverman, Joseph H. (1993). "Integer points, Diophantine approximation, and iteration of rational maps". Duke Mathematical Journal. 71 (3): 793–829. doi:10.1215/S0012-7094-93-07129-3. MR 1240603.
Zhang, Shou-Wu (2006). "Distributions in algebraic dynamics". In Yau, Shing Tung (ed.). Differential Geometry: A Tribute to Professor S.-S. Chern. Surveys in Differential Geometry. Vol. 10. Somerville, MA: International Press. pp. 381–430. doi:10.4310/SDG.2005.v10.n1.a9. ISBN 978-1-57146-116-2. MR 2408228.
Rumely, Robert; Baker, Matthew (2010). Potential theory and dynamics on the Berkovich projective line. Mathematical Surveys and Monographs. Vol. 159. Providence, RI: American Mathematical Society. arXiv:math/0407433. doi:10.1090/surv/159. ISBN 978-0-8218-4924-8. MR 2599526.
Granville, Andrew; Rudnick, Zeév, eds. (2007). Equidistribution in number theory, an introduction. NATO Science Series II: Mathematics, Physics and Chemistry. Vol. 237. Dordrecht: Springer Netherlands. doi:10.1007/978-1-4020-5404-4. ISBN 978-1-4020-5403-7. MR 2290490.
Sidorov, Nikita (2003). "Arithmetic dynamics". In Bezuglyi, Sergey; Kolyada, Sergiy (eds.). Topics in dynamics and ergodic theory. Survey papers and mini-courses presented at the international conference and US-Ukrainian workshop on dynamical systems and ergodic theory, Katsiveli, Ukraine, August 21–30, 2000. Lond. Math. Soc. Lect. Note Ser. Vol. 310. Cambridge: Cambridge University Press. pp. 145–189. doi:10.1017/CBO9780511546716.010. ISBN 0-521-53365-1. MR 2052279. S2CID 15482676. Zbl 1051.37007.

arxiv.org

Flynn, Eugene V.; Poonen, Bjorn; Schaefer, Edward F. (1997). "Cycles of quadratic polynomials and rational points on a genus-2 curve". Duke Mathematical Journal. 90 (3): 435–463. arXiv:math/9508211. doi:10.1215/S0012-7094-97-09011-6. MR 1480542. S2CID 15169450.
Stoll, Michael (2008). "Rational 6-cycles under iteration of quadratic polynomials". LMS Journal of Computation and Mathematics. 11: 367–380. arXiv:0803.2836. Bibcode:2008arXiv0803.2836S. doi:10.1112/S1461157000000644. MR 2465796. S2CID 14082110.
Rumely, Robert; Baker, Matthew (2010). Potential theory and dynamics on the Berkovich projective line. Mathematical Surveys and Monographs. Vol. 159. Providence, RI: American Mathematical Society. arXiv:math/0407433. doi:10.1090/surv/159. ISBN 978-0-8218-4924-8. MR 2599526.

doi.org

Silverman, Joseph H. (2007). The Arithmetic of Dynamical Systems. Graduate Texts in Mathematics. Vol. 241. New York: Springer. doi:10.1007/978-0-387-69904-2. ISBN 978-0-387-69903-5. MR 2316407.
Northcott, Douglas Geoffrey (1950). "Periodic points on an algebraic variety". Annals of Mathematics. 51 (1): 167–177. doi:10.2307/1969504. JSTOR 1969504. MR 0034607.
Morton, Patrick; Silverman, Joseph H. (1994). "Rational periodic points of rational functions". International Mathematics Research Notices. 1994 (2): 97–110. doi:10.1155/S1073792894000127. MR 1264933.
Morton, Patrick (1992). "Arithmetic properties of periodic points of quadratic maps". Acta Arithmetica. 62 (4): 343–372. doi:10.4064/aa-62-4-343-372. MR 1199627.
Flynn, Eugene V.; Poonen, Bjorn; Schaefer, Edward F. (1997). "Cycles of quadratic polynomials and rational points on a genus-2 curve". Duke Mathematical Journal. 90 (3): 435–463. arXiv:math/9508211. doi:10.1215/S0012-7094-97-09011-6. MR 1480542. S2CID 15169450.
Stoll, Michael (2008). "Rational 6-cycles under iteration of quadratic polynomials". LMS Journal of Computation and Mathematics. 11: 367–380. arXiv:0803.2836. Bibcode:2008arXiv0803.2836S. doi:10.1112/S1461157000000644. MR 2465796. S2CID 14082110.
Poonen, Bjorn (1998). "The classification of rational preperiodic points of quadratic polynomials over $Q$ : a refined conjecture". Mathematische Zeitschrift. 228 (1): 11–29. doi:10.1007/PL00004405. MR 1617987. S2CID 118160396.
Silverman, Joseph H. (1993). "Integer points, Diophantine approximation, and iteration of rational maps". Duke Mathematical Journal. 71 (3): 793–829. doi:10.1215/S0012-7094-93-07129-3. MR 1240603.
Zhang, Shou-Wu (2006). "Distributions in algebraic dynamics". In Yau, Shing Tung (ed.). Differential Geometry: A Tribute to Professor S.-S. Chern. Surveys in Differential Geometry. Vol. 10. Somerville, MA: International Press. pp. 381–430. doi:10.4310/SDG.2005.v10.n1.a9. ISBN 978-1-57146-116-2. MR 2408228.
Rumely, Robert; Baker, Matthew (2010). Potential theory and dynamics on the Berkovich projective line. Mathematical Surveys and Monographs. Vol. 159. Providence, RI: American Mathematical Society. arXiv:math/0407433. doi:10.1090/surv/159. ISBN 978-0-8218-4924-8. MR 2599526.
Granville, Andrew; Rudnick, Zeév, eds. (2007). Equidistribution in number theory, an introduction. NATO Science Series II: Mathematics, Physics and Chemistry. Vol. 237. Dordrecht: Springer Netherlands. doi:10.1007/978-1-4020-5404-4. ISBN 978-1-4020-5403-7. MR 2290490.
Sidorov, Nikita (2003). "Arithmetic dynamics". In Bezuglyi, Sergey; Kolyada, Sergiy (eds.). Topics in dynamics and ergodic theory. Survey papers and mini-courses presented at the international conference and US-Ukrainian workshop on dynamical systems and ergodic theory, Katsiveli, Ukraine, August 21–30, 2000. Lond. Math. Soc. Lect. Note Ser. Vol. 310. Cambridge: Cambridge University Press. pp. 145–189. doi:10.1017/CBO9780511546716.010. ISBN 0-521-53365-1. MR 2052279. S2CID 15482676. Zbl 1051.37007.

harvard.edu

ui.adsabs.harvard.edu

Stoll, Michael (2008). "Rational 6-cycles under iteration of quadratic polynomials". LMS Journal of Computation and Mathematics. 11: 367–380. arXiv:0803.2836. Bibcode:2008arXiv0803.2836S. doi:10.1112/S1461157000000644. MR 2465796. S2CID 14082110.

jstor.org

Northcott, Douglas Geoffrey (1950). "Periodic points on an algebraic variety". Annals of Mathematics. 51 (1): 167–177. doi:10.2307/1969504. JSTOR 1969504. MR 0034607.

semanticscholar.org

api.semanticscholar.org

Flynn, Eugene V.; Poonen, Bjorn; Schaefer, Edward F. (1997). "Cycles of quadratic polynomials and rational points on a genus-2 curve". Duke Mathematical Journal. 90 (3): 435–463. arXiv:math/9508211. doi:10.1215/S0012-7094-97-09011-6. MR 1480542. S2CID 15169450.
Stoll, Michael (2008). "Rational 6-cycles under iteration of quadratic polynomials". LMS Journal of Computation and Mathematics. 11: 367–380. arXiv:0803.2836. Bibcode:2008arXiv0803.2836S. doi:10.1112/S1461157000000644. MR 2465796. S2CID 14082110.
Poonen, Bjorn (1998). "The classification of rational preperiodic points of quadratic polynomials over $Q$ : a refined conjecture". Mathematische Zeitschrift. 228 (1): 11–29. doi:10.1007/PL00004405. MR 1617987. S2CID 118160396.
Sidorov, Nikita (2003). "Arithmetic dynamics". In Bezuglyi, Sergey; Kolyada, Sergiy (eds.). Topics in dynamics and ergodic theory. Survey papers and mini-courses presented at the international conference and US-Ukrainian workshop on dynamical systems and ergodic theory, Katsiveli, Ukraine, August 21–30, 2000. Lond. Math. Soc. Lect. Note Ser. Vol. 310. Cambridge: Cambridge University Press. pp. 145–189. doi:10.1017/CBO9780511546716.010. ISBN 0-521-53365-1. MR 2052279. S2CID 15482676. Zbl 1051.37007.

zbmath.org

Sidorov, Nikita (2003). "Arithmetic dynamics". In Bezuglyi, Sergey; Kolyada, Sergiy (eds.). Topics in dynamics and ergodic theory. Survey papers and mini-courses presented at the international conference and US-Ukrainian workshop on dynamical systems and ergodic theory, Katsiveli, Ukraine, August 21–30, 2000. Lond. Math. Soc. Lect. Note Ser. Vol. 310. Cambridge: Cambridge University Press. pp. 145–189. doi:10.1017/CBO9780511546716.010. ISBN 0-521-53365-1. MR 2052279. S2CID 15482676. Zbl 1051.37007.