Investigación doctoral
Bibliografía
Bibliografía
Referencias y fuentes de mi investigación sobre la conjetura de Collatz y la dinámica simbólica. Cada entrada lleva etiquetas —tipo, área, MSC, dificultad de lectura, acceso e importancia para la tesis—; pulsa cualquier cualidad para ver solo esa bibliografía, como en los problemas por tema del Cangur.
Filtrar por
- [1]Althöfer, I. (2020). Lothar Collatz zwischen 1933 und 1950 – Eine Teilbiographie. 3-Hirn-Verlag. enlace ↗
- [2]Applegate, D. & Lagarias, J. C. (2003). Lower bounds for the total stopping time of 3x+1 iterates. Math. Comp. 72(242), 1035–1049.
- [3]Bařina, D. (2025). Improved verification limit for the convergence of the Collatz conjecture. The Journal of Supercomputing. enlace ↗
- [4]Belaga, E. G. & Mignotte, M. (1998). Embedding the 3x+1 conjecture in a 3x+d context. Experimental Mathematics 7(2), 145–151. enlace ↗
- [5]Belaga, E. G. & Mignotte, M. (2006). The Collatz problem and its generalizations: experimental data. Table 1: primitive cycles of (3n+d)-mappings. Prépublication IRMA, Strasbourg (HAL). enlace ↗
- [6]Bennett, M. A. & de Weger, B. M. M. (1998). On the Diophantine equation |axn−byn|=1. Math. Comp. 67(221), 413–438.
- [7]Bernstein, D. J. & Lagarias, J. C. (1996). The 3x+1 conjugacy map. Canadian Journal of Mathematics 48(6), 1154–1169.
- [8]Böhm, C. & Sontacchi, G. (1978). On the existence of cycles of given length in integer sequences like xn+1=xn/2 if xn even, and xn+1=3xn+1 otherwise. Atti Accad. Naz. Lincei (8) 64(3), 260–264.
- [9]Chamberland, M. (2003). An update on the 3x+1 problem. Butlletí de la Societat Catalana de Matemàtiques 18, 19–45.
- [10]Collatz, L. & Sinogowitz, U. (1957). Spektren endlicher Grafen. Abh. Math. Sem. Univ. Hamburg 21, 63–77.
- [11]Collatz, L. (1942). Einschließungssatz für die charakteristischen Zahlen von Matrizen. Math. Z. 48, 221–226.
- [12]Collatz, L. (1986). On the motivation and origin of the (3n+1)-problem. En J. C. Lagarias (Ed.), The Ultimate Challenge: The 3x+1 Problem (pp. 241–247). AMS, 2010. enlace ↗
- [13]Coxeter, H. S. M. (1971). Cyclic sequences and frieze patterns. Vinculum 8, 4–7. [Reimpr. en The Ultimate Challenge, AMS 2010, 211–218.] enlace ↗
- [14]Crandall, R. E. (1978). On the “3x+1” problem. Math. Comp. 32(144), 1281–1292.
- [15]Cvetković, D., Doob, M. & Sachs, H. (1995). Spectra of Graphs. Theory and Applications (3.ª ed.). Johann Ambrosius Barth.
- [16]Eliahou, S. (1993). The 3x+1 problem: new lower bounds on nontrivial cycle lengths. Discrete Mathematics 118(1–3), 45–56.
- [17]Everett, C. J. (1977). Iteration of the number-theoretic function f(2n)=n, f(2n+1)=3n+2. Advances in Mathematics 25(1), 42–45.
- [18]Gardner, M. (1972). Mathematical Games. Scientific American 226(6), 114–118.
- [19]Garner, L. E. (1985). On heights in the Collatz 3n+1 problem. Discrete Mathematics 55(1), 57–64.
- [20]Guy, R. K. (1983). Don't try to solve these problems! American Mathematical Monthly 90(1), 35–41. enlace ↗
- [21]Hayes, B. (1984). Computer recreations: The ups and downs of hailstone numbers. Scientific American 250(1), 10–16.
- [22]Holden, D. (2018). Results on the 3x+1 and 3x+d conjectures. Fibonacci Quarterly (preprint, CSU Fresno).
- [23]Karras, I. & de Weger, B. M. M. (2026). Modular Collatz graphs (Determinants of Modular Collatz Graphs and Variants). Preprint, arXiv:2601.15463. enlace ↗
- [24]Krasikov, I. & Lagarias, J. C. (2003). Bounds for the 3x+1 problem using difference inequalities. Acta Arithmetica 109(3), 237–258.
- [25]Laarhoven, T. & de Weger, B. (2013). The Collatz conjecture and De Bruijn graphs. Indagationes Mathematicae (N.S.) 24(4), 971–983. enlace ↗
- [26]Lagarias, J. C. (1985). The 3x+1 problem and its generalizations. American Mathematical Monthly 92(1), 3–23. enlace ↗
- [27]Lagarias, J. C. (1990). The set of rational cycles for the 3x+1 problem. Acta Arithmetica 56(1), 33–53.
- [28]Lagarias, J. C. (2003). The 3x+1 problem: an annotated bibliography (1963–1999). arXiv:math/0309224. enlace ↗
- [29]Lagarias, J. C. (2010). The 3x+1 problem: an overview. En The Ultimate Challenge, AMS, 3–29. (arXiv:2111.02635.) enlace ↗
- [30]Lagarias, J. C. (Ed.) (2010). The Ultimate Challenge: The 3x+1 Problem. American Mathematical Society. enlace ↗
- [31]Lang, W. (2014). On Collatz words, sequences and trees. Journal of Integer Sequences 17, Art. 14.11.7. enlace ↗
- [32]Laurent, M., Mignotte, M. & Nesterenko, Y. (1995). Formes linéaires en deux logarithmes et déterminants d'interpolation. Journal of Number Theory 55(2), 285–321.
- [33]Lind, D. & Marcus, B. (1995). An Introduction to Symbolic Dynamics and Coding. Cambridge University Press. enlace ↗
- [34]Mathematics Genealogy Project, id 20676 (Lothar Collatz). enlace ↗
- [35]Matthews, K. R. & Watts, A. M. (1984). A generalization of Hasse's generalization of the Syracuse algorithm. Acta Arithmetica 43(2), 167–175.
- [36]Monks, K. G. (2006). The sufficiency of arithmetic progressions for the 3x+1 conjecture. Proceedings of the AMS 134(10), 2861–2872. enlace ↗
- [37]Moreau, C. (1872). Sur les permutations circulaires distinctes. Nouvelles Annales de Mathématiques (2) 11, 309–314. enlace ↗
- [38]O'Connor, J. J. & Robertson, E. F. (2006). Lothar Collatz. MacTutor, Univ. of St Andrews. enlace ↗
- [39]Oliveira e Silva, T. (1999). Maximum excursion and stopping time record-holders for the 3x+1 problem: computational results. Math. Comp. 68(225), 371–384. enlace ↗
- [40]Reutenauer, C. (1993). Free Lie Algebras. Oxford University Press.
- [41]Sander, J. W. (1990). On the (3N+1)-conjecture. Acta Arithmetica 55(3), 241–248.
- [42]Segal, S. L. (2003). Mathematicians under the Nazis. Princeton University Press.
- [43]Simons, J. L. & de Weger, B. (2005). Theoretical and computational bounds for m-cycles of the 3n+1 problem. Acta Arithmetica 117(1), 51–70. enlace ↗
- [44]Simons, J. L. (2005). On the nonexistence of 2-cycles for the 3x+1 problem. Math. Comp. 74, 1565–1572. enlace ↗
- [45]Simons, J. L. (2008). On the (non-)existence of m-cycles for generalized Syracuse sequences. Acta Arithmetica 131(3), 217–254. enlace ↗
- [46]Steiner, R. P. (1978). A theorem on the Syracuse problem. Proc. 7th Manitoba Conf. on Numerical Mathematics and Computing, 553–559.
- [47]Tao, T. (2022). Almost all orbits of the Collatz map attain almost bounded values. Forum of Mathematics, Pi 10, e12. enlace ↗
- [48]Terras, R. (1976). A stopping time problem on the positive integers. Acta Arithmetica 30(3), 241–252.
- [49]Thwaites, B. (1985). My conjecture. Bull. Inst. Math. Appl. 21, 35–41.
- [50]Tremblay, R. (2020). Generalized 3x+1 mappings: counting cycles. arXiv:2008.11103. enlace ↗
- [51]Wirsching, G. J. (1996). On the combinatorial structure of 3N+1 predecessor sets. Discrete Mathematics 148(1–3), 265–286.
- [52]Wirsching, G. J. (1998). The Dynamical System Generated by the 3n+1 Function. Springer, Lecture Notes in Mathematics 1681. enlace ↗