J. Abrial, W. Su, and H. Zhu, Formalizing Hybrid Systems with Event-B, ASM. LNCS, pp.178-193, 2012.
DOI : 10.1007/978-3-642-30885-7_13

S. Bak, S. Bogomolov, and T. T. Johnson, HYST, Proceedings of the 18th International Conference on Hybrid Systems Computation and Control, HSCC '15, pp.128-133, 2015.
DOI : 10.1145/2728606.2728630

M. Berz and K. Makino, Verified integration of odes and flows using differential algebraic methods on high-order taylor models, Reliable Computing, vol.4, issue.4, pp.361-369, 1998.
DOI : 10.1023/A:1024467732637

G. E. Collins, Hauptvortrag: Quantifier elimination for real closed fields by cylindrical algebraic decomposition In: Automata Theory and Formal Languages, 2nd GI Conference, LNCS, vol.33, pp.134-183, 1975.
DOI : 10.1007/978-3-7091-9459-1_4

R. Conti and M. Galeotti, Dynamical Systems, chap. Totally Bounded Cubic Systems in R 2, pp.103-171, 2003.

F. Dumortier, J. Llibre, and J. C. Artés, Qualitative Theory of Planar Differential Systems, 2006.

K. Ghorbal and A. Platzer, Characterizing Algebraic Invariants by Differential Radical Invariants, TACAS. LNCS, pp.279-294, 2014.
DOI : 10.1007/978-3-642-54862-8_19

J. M. Ginoux, Differential Geometry Applied to Dynamical Systems, World Scientific Series on Nonlinear Science World Scientific, vol.66, 2009.
DOI : 10.1142/7333

URL : https://hal.archives-ouvertes.fr/hal-01101601

A. Girard and G. J. Pappas, Approximate Bisimulation: A Bridge Between Computer Science and Control Theory, European Journal of Control, vol.17, issue.5-6, pp.5-6, 2011.
DOI : 10.3166/ejc.17.568-578

URL : https://hal.archives-ouvertes.fr/hal-00765660

A. Goriely, Integrability and Nonintegrability of Dynamical Systems Advanced series in nonlinear dynamics, World Scientific, 2001.

J. K. Hale and J. P. Lasalle, Differential Equations: Linearity vs. Nonlinearity, SIAM Review, vol.5, issue.3, pp.249-272, 1963.
DOI : 10.1137/1005068

Z. Han and B. Krogh, Reachability analysis of hybrid control systems using reducedorder models, Proceedings of the 2004, pp.1183-1189, 2004.

J. Jeannin, K. Ghorbal, Y. Kouskoulas, R. Gardner, A. Schmidt et al., A formally verified hybrid system for safe advisories in the next-generation airborne collision avoidance system, TACAS. LNCS, pp.21-36, 2015.
DOI : 10.1007/978-3-642-05089-3_35

URL : https://hal.archives-ouvertes.fr/hal-01232365

T. T. Johnson, J. Green, S. Mitra, R. Dudley, and R. S. Erwin, Satellite Rendezvous and Conjunction Avoidance: Case Studies in Verification of Nonlinear Hybrid Systems, FM 2012: Formal Methods -18th International Symposium. Proceedings. LNCS, pp.252-266, 2012.
DOI : 10.1007/978-3-642-32759-9_22

N. Matringe, A. V. Moura, and R. Rebiha, Generating Invariants for Non-linear Hybrid Systems by Linear Algebraic Methods, SAS. LNCS, pp.373-389, 2010.
DOI : 10.1007/978-3-642-15769-1_23

N. S. Nedialkov, Interval Tools for ODEs and DAEs, 12th GAMM -IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN). pp, pp.4-4, 2006.

M. Neher, K. R. Jackson, and N. S. Nedialkov, On Taylor Model Based Integration of ODEs, SIAM Journal on Numerical Analysis, vol.45, issue.1, pp.236-262, 2007.
DOI : 10.1137/050638448

G. J. Pappas, Bisimilar linear systems, Automatica, vol.39, issue.12, pp.2035-2047, 2003.
DOI : 10.1016/j.automatica.2003.07.003

A. Platzer, A Complete Uniform Substitution Calculus for Differential Dynamic Logic, Journal of Automated Reasoning, vol.89, issue.1, pp.1-47, 2016.
DOI : 10.1007/978-3-540-71070-7_15

A. Platzer and E. M. Clarke, Formal Verification of Curved Flight Collision Avoidance Maneuvers: A Case Study, FM. LNCS, pp.547-562, 2009.
DOI : 10.1007/978-3-642-05089-3_35

J. C. Robinson, An introduction to ordinary differential equations, 2004.
DOI : 10.1017/CBO9780511801204

S. Sankaranarayanan, Change-of-bases abstractions for non-linear hybrid systems, Nonlinear Analysis: Hybrid Systems, vol.19, pp.107-133, 2016.
DOI : 10.1016/j.nahs.2015.08.006

S. Sankaranarayanan, H. B. Sipma, and Z. Manna, Constructing invariants for hybrid systems, Formal Methods in System Design, vol.96, issue.2, pp.25-55, 2008.
DOI : 10.1007/s10703-007-0046-1

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.2632

S. Sankaranarayanan and A. Tiwari, Relational Abstractions for Continuous and Hybrid Systems, CAV. LNCS, pp.686-702, 2011.
DOI : 10.1007/s10703-007-0044-3

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.226.5943

S. H. Strogatz, Nonlinear Dynamics and Chaos, 1994.

A. Tarski, A Decision Method for Elementary Algebra and Geometry, Bulletin of the American Mathematical Society, vol.59, 1951.
DOI : 10.1007/978-3-7091-9459-1_3

G. Teschl, Ordinary Differential Equations and Dynamical Systems, Graduate Studies in Mathematics, vol.140, 2012.
DOI : 10.1090/gsm/140

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.304.2428

H. Zhao, M. Yang, N. Zhan, B. Gu, L. Zou et al., Formal Verification of a Descent Guidance Control Program of a Lunar Lander, FM. LNCS, pp.733-748, 2014.
DOI : 10.1007/978-3-319-06410-9_49

L. Zou, J. Lv, S. Wang, N. Zhan, T. Tang et al., Verifying Chinese Train Control System under a Combined Scenario by Theorem Proving, VSTTE. LNCS, pp.262-280, 2013.
DOI : 10.1007/978-3-642-54108-7_14