74
G. Gubbiotti
References
1. V.E. Adler, On a discrete analog of the Tzitzeica equation. Preprint (2011). arXiv:1103.5139
2. V.E. Adler, Integrable Möbius invariant evolutionary lattices of second order. Preprint (2016).
arXiv:1605.00018
3. V.E. Adler, Integrability test for evolutionary lattice equations of higher order. J. Symb.
Comput. 74, 125–139 (2016)
4. V.I. Arnol’d, Dynamics of complexity of intersections. Bol. Soc. Brasil. Mat. (N.S.) 21, 1–10
(1990)
5. M. Bellon, C.M. Viallet, Algebraic entropy. Commun. Math. Phys. 204, 425–437 (1999)
6. M. Bruschi, O. Ragnisco, P.M. Santini, G.Z. Tu, Integrable symplectic maps. Physica D 49(3),
273–294 (1991)
7. H.W. Capel, R. Sahadevan, A new family of four-dimensional symplectic and integrable
mappings. Physica A 289, 80–106 (2001)
8. E. Celledoni, C. Evripidou, D.I. McLaren, B. Owren, G.R.W. Quispel, B.K. Tapley, P.H.
van der Kamp, Using discrete Darboux polynomials to detect and determine preserved
measures and integrals of rational maps. J. Phys. A Math. Theor. 52, 31LT01 (11pp) (2019)
9. D.K. Demskoi, D.T. Tran, P.H. van der Kamp, G.R.W. Quispel, A novel nth order difference
equation that may be integrable. J. Phys. A 45, 135,202, (10pp) (2012)
10. D.K. Demskoy, C.M. Viallet, Algebraic entropy for semi-discrete equations. J. Phys. A Math.
Theor. 45, 352,001 (10 pp) (2012)
11. J. Duistermaat, Discrete Integrable Systems: QRT Maps and Elliptic Surfaces. Springer
Monographs in Mathematics (Springer, New York, 2011)
12. S. Elaydi, An Introduction to Difference Equations, 3rd edn. (Springer, 2005)
13. G. Falqui, C.M. Viallet, Singularity, complexity, and quasi-integrability of rational mappings.
Commun. Math. Phys. 154, 111–125 (1993)
14. P. Flajolet, A. Odlyzko, Singularity analysis of generating functions. SIAM J. Discr. Math.
3(2), 216–240 (1990)
15. R.N. Garifullin, R.I. Yamilov, D. Levi, Classification of five-point differential-difference
equations. J. Phys. A Math. Theor. 50, 125,201 (27pp) (2017)
16. R.N. Garifullin, R.I. Yamilov, D. Levi, Classification of five-point differential-difference
equations II. J. Phys. A Math. Theor. 51, 065,204 (16pp) (2018)
17. B. Grammaticos, R.G. Halburd, A. Ramani, C.M. Viallet, How to detect the integrability of
discrete systems. J. Phys. A Math. Theor. 42, 454,002 (41 pp) (2009). Newton Institute Preprint
NI09060-DIS
18. G. Gubbiotti, Integrability of difference equations through algebraic entropy and generalized
symmetries, in Symmetries and Integrability of Difference Equations: Lecture Notes of the
Abecederian School of SIDE 12, Montreal 2016, ed. by D. Levi, R. Verge-Rebelo, P. Winternitz.
CRM Series in Mathematical Physics, chap. 3 (Springer International Publishing, Berlin,
2017), pp. 75–152
19. G. Gubbiotti, Algebraic entropy of a class of five-point differential-difference equations.
Symmetry 11, 432 (24pp) (2019)
20. G. Gubbiotti, Stationary reductions of five-point differential-difference equations and their
integrability properties (2020). In preparation
21. G. Gubbiotti, N. Joshi, D.T. Tran, C.M. Viallet, Complexity and integrability in 4D bi-rational
maps with two invariants (2020). Accepted for publication in Springer’s PROMS series:
“Asymptotic, Algebraic and Geometric Aspects of Integrable Systems”
22. G. Gubbiotti, N. Joshi, D.T. Tran, C.M. Viallet, Bi-rational maps in four dimensions with two
invariants. J. Phys. A: Math. Theor 53, 115201 (24pp) (2020)
23. A. Hagar, Discrete or Continuous? The Quest for Fundamental Length in Modern Physics
(Cambridge University Press, Cambridge, 2014)
24. J. Hietarinta, N. Joshi, F. Nijhoff, Discrete Systems and Integrability. Cambridge Texts in
Applied Mathematics (Cambridge University Press, 2016)
G. Gubbiotti
References
1. V.E. Adler, On a discrete analog of the Tzitzeica equation. Preprint (2011). arXiv:1103.5139
2. V.E. Adler, Integrable Möbius invariant evolutionary lattices of second order. Preprint (2016).
arXiv:1605.00018
3. V.E. Adler, Integrability test for evolutionary lattice equations of higher order. J. Symb.
Comput. 74, 125–139 (2016)
4. V.I. Arnol’d, Dynamics of complexity of intersections. Bol. Soc. Brasil. Mat. (N.S.) 21, 1–10
(1990)
5. M. Bellon, C.M. Viallet, Algebraic entropy. Commun. Math. Phys. 204, 425–437 (1999)
6. M. Bruschi, O. Ragnisco, P.M. Santini, G.Z. Tu, Integrable symplectic maps. Physica D 49(3),
273–294 (1991)
7. H.W. Capel, R. Sahadevan, A new family of four-dimensional symplectic and integrable
mappings. Physica A 289, 80–106 (2001)
8. E. Celledoni, C. Evripidou, D.I. McLaren, B. Owren, G.R.W. Quispel, B.K. Tapley, P.H.
van der Kamp, Using discrete Darboux polynomials to detect and determine preserved
measures and integrals of rational maps. J. Phys. A Math. Theor. 52, 31LT01 (11pp) (2019)
9. D.K. Demskoi, D.T. Tran, P.H. van der Kamp, G.R.W. Quispel, A novel nth order difference
equation that may be integrable. J. Phys. A 45, 135,202, (10pp) (2012)
10. D.K. Demskoy, C.M. Viallet, Algebraic entropy for semi-discrete equations. J. Phys. A Math.
Theor. 45, 352,001 (10 pp) (2012)
11. J. Duistermaat, Discrete Integrable Systems: QRT Maps and Elliptic Surfaces. Springer
Monographs in Mathematics (Springer, New York, 2011)
12. S. Elaydi, An Introduction to Difference Equations, 3rd edn. (Springer, 2005)
13. G. Falqui, C.M. Viallet, Singularity, complexity, and quasi-integrability of rational mappings.
Commun. Math. Phys. 154, 111–125 (1993)
14. P. Flajolet, A. Odlyzko, Singularity analysis of generating functions. SIAM J. Discr. Math.
3(2), 216–240 (1990)
15. R.N. Garifullin, R.I. Yamilov, D. Levi, Classification of five-point differential-difference
equations. J. Phys. A Math. Theor. 50, 125,201 (27pp) (2017)
16. R.N. Garifullin, R.I. Yamilov, D. Levi, Classification of five-point differential-difference
equations II. J. Phys. A Math. Theor. 51, 065,204 (16pp) (2018)
17. B. Grammaticos, R.G. Halburd, A. Ramani, C.M. Viallet, How to detect the integrability of
discrete systems. J. Phys. A Math. Theor. 42, 454,002 (41 pp) (2009). Newton Institute Preprint
NI09060-DIS
18. G. Gubbiotti, Integrability of difference equations through algebraic entropy and generalized
symmetries, in Symmetries and Integrability of Difference Equations: Lecture Notes of the
Abecederian School of SIDE 12, Montreal 2016, ed. by D. Levi, R. Verge-Rebelo, P. Winternitz.
CRM Series in Mathematical Physics, chap. 3 (Springer International Publishing, Berlin,
2017), pp. 75–152
19. G. Gubbiotti, Algebraic entropy of a class of five-point differential-difference equations.
Symmetry 11, 432 (24pp) (2019)
20. G. Gubbiotti, Stationary reductions of five-point differential-difference equations and their
integrability properties (2020). In preparation
21. G. Gubbiotti, N. Joshi, D.T. Tran, C.M. Viallet, Complexity and integrability in 4D bi-rational
maps with two invariants (2020). Accepted for publication in Springer’s PROMS series:
“Asymptotic, Algebraic and Geometric Aspects of Integrable Systems”
22. G. Gubbiotti, N. Joshi, D.T. Tran, C.M. Viallet, Bi-rational maps in four dimensions with two
invariants. J. Phys. A: Math. Theor 53, 115201 (24pp) (2020)
23. A. Hagar, Discrete or Continuous? The Quest for Fundamental Length in Modern Physics
(Cambridge University Press, Cambridge, 2014)
24. J. Hietarinta, N. Joshi, F. Nijhoff, Discrete Systems and Integrability. Cambridge Texts in
Applied Mathematics (Cambridge University Press, 2016)