E. Asarin, O. Maler, and A. Pnueli, Reachability analysis of dynamical systems having piecewise-constant derivatives, Theoretical Computer Science, vol.138, issue.1, pp.35-65, 1995.
DOI : 10.1016/0304-3975(94)00228-B

S. Bellantoni and S. Cook, A new recursion-theoretic characterization of the polytime functions, Computational Complexity, vol.106, issue.2, pp.97-110, 1992.
DOI : 10.1007/BF01201998

L. Blum, M. Shub, and S. Smale, On a theory of computation and complexity over the real numbers: $NP$- completeness, recursive functions and universal machines, Bulletin of the American Mathematical Society, vol.21, issue.1, pp.1-46, 1989.
DOI : 10.1090/S0273-0979-1989-15750-9

O. Bournez and M. L. Campagnolo, New Computational Paradigms. Changing Conceptions of What is Computable, chapter A Survey on Continuous Time Computations, pp.383-423, 2008.

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, vol.23, issue.3, pp.317-335, 2007.
DOI : 10.1016/j.jco.2006.12.005

URL : https://hal.archives-ouvertes.fr/inria-00102947

O. Bournez and E. Hainry, Recursive analysis characterized as a class of real recursive functions, Fundamenta Informaticae, vol.74, issue.4, pp.409-433, 2006.
URL : https://hal.archives-ouvertes.fr/inria-00000515

V. Brattka, Computability over Topological Structures, Computability and Models, pp.93-136, 2003.
DOI : 10.1007/978-1-4615-0755-0_5

L. Manuel, C. Campagnolo, J. Moore, and . Costa, An analog characterization of the Grzegorczyk hierarchy, Journal of Complexity, vol.18, issue.4, pp.977-1000, 2002.

L. Manuel, K. Campagnolo, and . Ojakian, The methods of approximation and lifting in real computation, In Computability and Complexity in Analysis Electronic Notes in Theoretical Computer Science, vol.167, pp.387-423, 2006.

P. Clote, Computational models and function algebras, Handbook of Computability Theory, pp.589-681, 1998.

A. Cobham, The intrinsic computational difficulty of functions, Proceedings of the International Conference on Logic, Methodology, and Philosophy of Science, pp.24-30, 1965.

S. Daniel, M. L. Graça, J. Campagnolo, and . Buescu, Robust simulations of Turing machines with analytic maps and flows, CiE 2005: New Computational Paradigms, pp.169-179, 2005.

S. Daniel, J. Graça, and . Costa, Analog computers and recursive functions over the reals, pp.644-664, 2003.

A. Grzegorczyk, On the definitions of computable real continuous functions, pp.61-71, 1957.

M. Hofmann, Type systems for polynomial-time computation, 1999.

N. D. Jones, The expressive power of higher-order types or, life without CONS, Journal of Functional Programming, vol.11, issue.1, pp.5-94, 2001.
DOI : 10.1017/S0956796800003889

M. Bruce, S. A. Kapron, and . Cook, A new characterization of type-2 feasibility, SIAM Journal on Computing, vol.25, issue.1, pp.117-132, 1996.

K. Ko, Complexity Theory of Real Functions, Birkhäuser, 1991.
DOI : 10.1007/978-1-4684-6802-1

D. Lacombe, Extension de la notion de fonction récursive aux fonctions d'une ou plusieurs variables réelles III. Comptes Rendus de l'Académie des sciences Paris, pp.151-153, 1955.

J. Marion and J. Moyen, Efficient first order functional program interpreter with time bound certifications, LPAR, pp.25-42, 1955.
URL : https://hal.archives-ouvertes.fr/inria-00099178

C. Moore, Dynamical recognizers: real-time language recognition by analog computers, Theoretical Computer Science, vol.201, issue.1-2, pp.99-136, 1998.
DOI : 10.1016/S0304-3975(97)00028-5

URL : http://doi.org/10.1016/s0304-3975(97)00028-5

K. Ruohonen, Event detection for ODES and nonrecursive hierarchies, Proceedings of the Colloquium in Honor of Arto Salomaa, pp.358-371, 1994.
DOI : 10.1007/3-540-58131-6_59

C. E. Shannon, Mathematical Theory of the Differential Analyzer, Journal of Mathematics and Physics, vol.XXII, issue.1-4, pp.337-354, 1941.
DOI : 10.1002/sapm1941201337

A. M. Turing, On computable numbers, with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, pp.230-265, 1936.

K. Weihrauch, Computable Analysis: an Introduction, 2000.