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D. S. Graça and N. Zhong. Computability of Ordinary Differential Equations.

*Proceedings of the 14th Conference on Computability in Europe, CiE 2018: Sailing Routes in the World of Computation*. In F. Manea, R. Miller, and D. Nowotka editors, volume 10936 of*Lecture Notes in Computer Science*, pages 204-213, Springer, 2018.**Get:**Published version or PreprintD. S. Graça, C. Rojas, and N. Zhong. Computing geometric Lorenz attractors with arbitrary precision.

*Transactions of the American Mathematical Society*, 370:2955-2970, 2018.**Get:**Published version or PreprintO. Bournez, D. S. Graça, and A. Pouly. Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length.

*Journal of the ACM*, 64(6), ACM 2017.**Get:**Published version or PreprintO. Bournez, D. S. Graça, and A. Pouly. On the Functions Generated by the General Purpose Analog Computer.

*Information and Computation*, 257:34-57, Elsevier 2017.**Get:**Published version or PreprintO. Bournez, D. S. Graça, and A. Pouly. Computing with Polynomial Ordinary Differential Equations.

*Journal of Complexity*, 36:106-140, Elsevier 2016.**Get:**Published version or PreprintO. Bournez, D. S. Graça, and A. Pouly. Polynomial Time Corresponds to Solutions of Polynomial Ordinary Differential Equations of Polynomial Length - The General Purpose Analog Computer and Computable Analysis are two efficiently equivalent models of computations.

*Proceedings of the 43rd International Colloquium on Automata, Languages and Programming (ICALP 2016)*. In I. Chatzigiannakis, M. Mitzenmacher, Y. Rabani, D. Sangiorgi editors, volume 55 of*Leibniz International Proceedings in Informatics (LIPIcs)*, pages 109:1-109:15, Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2016.**Best paper award**(Track B).**Get:**Published version or PreprintA. Pouly and D. S. Graça. Computational complexity of solving polynomial differential equations over unbounded domains.

*Theoretical Computer Science*, 626(2):67-82, Elsevier 2016.**Get:**Published version or PreprintO. Bournez, D. S. Graça, A. Pouly. Rigorous numerical computation of polynomial differential equations over unbounded domains.

*Proceedings of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences (MACIS 2015)*. In I. S. Kotsireas, S. M. Rump, C. K. Yap editors, volume 9582 of*Lecture Notes in Computer Science*, pages 469-473, Springer, 2016.**Get:**Published version or PreprintD. S. Graça and N. Zhong. An analytic system with a computable hyperbolic sink whose basin of attraction is non-computable.

*Theory of Computing Systems*, 57(2):478-520, Springer 2015.**Get:**Published version or PreprintO. Bournez, D. S. Graça, A. Pouly, and N. Zhong. Computability and computational complexity of the evolution of nonlinear dynamical systems.

*Proceedings of the 9th Conference on Computability in Europe, CiE 2013: The Nature of Computation — Logic, Algorithms, Applications*. In P. Bonizzoni, V. Brattka, B. Löwe editors, volume 7921 of*Lecture Notes in Computer Science*, pages 12-21, Springer, 2013.**Get:**Published version or PreprintD. S. Graça and A. Pouly. Computational complexity of adaptive methods for solving polynomial differential equations over unbounded domains.

*Proceedings of the 10th International Conference on Computability and Complexity in Analysis (CCA 2013)*. In M. Hoyrup, K.-I Ko, R. Rettinger, N. Zhong editors, pages 36-47, FernUniversität in Hagen, 2013.**Get:**PreprintO. Bournez, D. S. Graça, and A. Pouly. Turing machines can be efficiently simulated by the General Purpose Analog Computer.

*Proceedings of the 10th annual conference on Theory and Applications of Models of Computation (TAMC 2013)*. In FT-H. H. Chan, L. C. Lau, L. Trevisan editors, volume 7876 of*Lecture Notes in Computer Science*, pages 169-180, Springer, 2013.**Get:**Published version or PreprintO. Bournez, D. S. Graça, and E. Hainry. Computation with perturbed dynamical systems.

*Journal of Computer and System Sciences*, 79(5):714-724, Elsevier 2013.**Get:**Published version or PreprintD. S. Graça, N. Zhong, and J. Buescu. Computability, noncomputability, and hyperbolic systems.

*Applied Mathematics and Computation*, 219(6): 3039–3054, Elsevier, 2012.**Get:**Published version or PreprintD. S. Graça, N. Zhong, and H. S. Dumas. The connection between computability of a nonlinear problem and its linearization: the Hartman-Grobman theorem revisited.

*Theoretical Computer Science*, 457(26):101-110, Elsevier, 2012.**Get:**Published version or PreprintO. Bournez, D. S. Graça, and A. Pouly. On the complexity of solving polynomial initial value problems.

*Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation (ISSAC 2012), 2012*.**Get:**PreprintD. S. Graça. Non-computability, unpredictability, and financial markets.

*Complexity*, 17(6):24-30, Wiley, 2012.**Get:**Published version or Preprint-
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**Get:**Preprint O. Bournez, M. L. Campagnolo, D. S. Graça, and E. Hainry. Polynomial differential equations compute all real computable functions on computable compact intervals.

*Journal of Complexity*, 23:317-335, 2007.**Get:**Published version or PreprintD. S. Graça.

*Computability with Polynomial Differential Equations*. PhD thesis, IST, Universidade Técnica de Lisboa, 2007. Supervised by J. Buescu and M. L. Campagnolo.**Get:**Published versionO. Bournez, M. L. Campagnolo, D. S. Graça, and E. Hainry. The General Purpose Analog Computer and Computable Analysis are two equivalent paradigms of analog computation. In J.-Y. Cai, S. B. Cooper, and A. Li, editors,

*Theory and Applications of Models of Computation TAMC'06*, volume 3959 of*Lecture Notes in Computer Science*, pages 631-643. Springer, 2006.**Get:**Published version or PreprintD. S. Graça, N. Zhong, and J. Buescu. The ordinary differential equation defined by a computable function whose maximal interval of existence is non-computable. In G.Hanrot and P.Zimmermann, editors,

*Proceedings of the 7th Conference on Real Numbers and Computers (RNC 7)*, pages 33-40. LORIA/INRIA, 2006.**Get:**PreprintD. S. Graça, M. L. Campagnolo, and J. Buescu. Robust simulations of Turing machines with analytic maps and flows. In B. Cooper, B. Löwe, and L. Torenvliet, editors,

*Proceedings of CiE'05, New Computational Paradigms*, volume 3526 of*Lecture Notes in Computer Science*, pages 169-179. Springer, 2005.**Get:**Published version or PreprintD. S. Graça. Some recent developments on Shannon's General Purpose Analog Computer.

*Mathematical Logic Quarterly*, 50(4-5):473-485, 2004.**Get:**Published version or PreprintD. S. Graça. Computability via analog circuits. In V. Brattka, M. Schröder, K. Weihrauch, and N. Zhong, editors,

*Procs. International Conference on Computability and Complexity in Analysis*, pages 229-240. FernUniversität in Hagen, 2003.**Get:**PreprintD. S. Graça and J. F. Costa. Analog computers and recursive functions over the reals.

*Journal of Complexity*, 19(5):644-664, 2003.**Get:**Published version or PreprintD. S. Graça.

*The general purpose analog computer and recursive functions over the reals*Master's thesis, IST, Universidade Técnica de Lisboa, 2002. Supervised by J. F. Costa.**Get:**Published version