Die Stabilitätskriterien der elastomechanik, Arch Appl Mech, vol.20, pp.49-56, 1952. ,
DOI : 10.1007/bf00536796
The Routh-Hurwitz Condition for the Biquadratic Equation, Indagationes Mathematicae (Proceedings), vol.59, pp.403-409, 1956. ,
DOI : 10.1016/S1385-7258(56)50054-6
Paradoxes of dissipation-induced destabilization or who opened Whitney's umbrella? Z Angew Math Mech, pp.462-88, 2010. ,
ON MATRICES DEPENDING ON PARAMETERS, Russian Mathematical Surveys, vol.26, issue.2, pp.29-43, 1971. ,
DOI : 10.1070/RM1971v026n02ABEH003827
Functions on a crosscap, Mathematical Proceedings of the Cambridge Philosophical Society, vol.123, issue.1, pp.19-39, 1998. ,
DOI : 10.1017/S0305004197002132
THE BOUNDARY OF A SET OF STABLE MATRICES, Russian Mathematical Surveys, vol.35, issue.2, pp.249-50, 1070. ,
DOI : 10.1070/RM1980v035n02ABEH001651
On singularities of the boundary of a stability region, Mosc Univ Math Bull, vol.35, pp.19-22, 1980. ,
Variational Analysis of the Abscissa Mapping for Polynomials via the Gauss-Lucas Theorem, Journal of Global Optimization, vol.28, issue.3/4, pp.259-68, 2004. ,
DOI : 10.1023/B:JOGO.0000026448.63457.51
Dissipation-induced instabilities in finite dimensions, Reviews of Modern Physics, vol.79, issue.2, pp.519-53, 2007. ,
DOI : 10.1103/RevModPhys.79.519
THE SOLUTION OF SOME PERTURBATION PROBLEMS FOR MATRICES AND SELFADJOINT OR NON-SELFADJOINT DIFFERENTIAL EQUATIONS I, Russian Mathematical Surveys, vol.15, issue.3, pp.1-74, 1960. ,
DOI : 10.1070/RM1960v015n03ABEH004092
Perturbation theory of non-conjugate operators, USSR Computational Mathematics and Mathematical Physics, vol.6, issue.1, pp.73-8552, 1966. ,
DOI : 10.1016/0041-5553(66)90033-4
Analytic Perturbation Theory for Matrices and Operators (Operator Theory, Advances and Applications), vol.15, 1985. ,
On the Lidskii--Vishik--Lyusternik Perturbation Theory for Eigenvalues of Matrices with Arbitrary Jordan Structure, SIAM Journal on Matrix Analysis and Applications, vol.18, issue.4, pp.793-817, 1997. ,
DOI : 10.1137/S0895479895294666
Stability theory for dissipatively perturbed hamiltonian systems, Communications on Pure and Applied Mathematics, vol.1, issue.2, 1995. ,
DOI : 10.1002/cpa.3160480602
Nonconservative Stability Problems of Modern Physics Available online at, De Gruyter Studies in Mathematical Physics), vol.14, 2013. ,
Spectra and Pseudospectra, 2005. ,
DOI : 10.1007/978-3-662-03972-4_6
Ellipsoidal approximation of the stability domain of a polynomial, IEEE Transactions on Automatic Control, vol.48, issue.12, pp.2255-2264, 2003. ,
DOI : 10.1109/TAC.2003.820161
Inner Approximations for Polynomial Matrix Inequalities and Robust Stability Regions, IEEE Transactions on Automatic Control, vol.57, issue.6, pp.1456-67, 2011. ,
DOI : 10.1109/TAC.2011.2178717
URL : https://hal.archives-ouvertes.fr/hal-00588754
Lectures on bifurcations in versal families, Russ Math Surv, vol.27, pp.54-123, 1972. ,
DOI : 10.1007/978-3-642-31031-7_29
Zur korrekten Modellbildung in der Dynamik diskreter Systeme, Ingenieur-Archiv, vol.27, issue.1-2, pp.31-43, 1981. ,
DOI : 10.1007/BF00535953
Variational Analysis of the Abscissa Mapping for Polynomials, SIAM Journal on Control and Optimization, vol.39, issue.6, pp.1651-76, 2001. ,
DOI : 10.1137/S0363012900367655
Optimizing matrix stability, Proceedings of the American Mathematical Society, vol.129, issue.06, pp.1635-1677, 2001. ,
DOI : 10.1090/S0002-9939-00-05985-2
The mathematics of eigenvalue optimization, Mathematical Programming, vol.97, issue.1, pp.155-76, 2003. ,
DOI : 10.1007/s10107-003-0441-3
Variational analysis of functions of the roots of polynomials, Mathematical Programming, vol.46, issue.2-3, pp.263-92, 2005. ,
DOI : 10.1007/s10107-005-0616-1
Physics of Nonhermitian Degeneracies, Czechoslovak Journal of Physics, vol.54, issue.10, pp.1039-1086, 2004. ,
DOI : 10.1023/B:CJOP.0000044002.05657.04
The physics of exceptional points, Journal of Physics A: Mathematical and Theoretical, vol.45, issue.44, p.444016, 2012. ,
DOI : 10.1088/1751-8113/45/44/444016
Explicit Solutions for Root Optimization of a Polynomial Family With One Affine Constraint, IEEE Transactions on Automatic Control, vol.57, issue.12, pp.3078-89, 2012. ,
DOI : 10.1109/TAC.2012.2202069
Real matrices depending on parameters, Uspekhi Matematicheskih Nauk, pp.241-243, 1972. ,
Damped Oscillations of Linear Systems Available online at: http://www, Lecture Notes in Mathematics), vol.2023, pp.978-981, 2011. ,
On the Heavily Damped Response in Viscously Damped Dynamic Systems, Journal of Applied Mechanics, vol.71, issue.1, pp.131-135, 2004. ,
DOI : 10.1115/1.1629108
Overdamped and Gyroscopic Vibrating Systems, Journal of Applied Mechanics, vol.59, issue.1, pp.176-81, 1992. ,
DOI : 10.1115/1.2899425
The growth of a magnetic field in a three-dimensional steady incompressible flow, Mosc Univ Math Bull, vol.38, pp.50-54, 1983. ,
DOI : 10.1007/978-3-642-31031-7_38
Determining role of Krein signature for three-dimensional Arnold tongues of oscillatory dynamos, Physical Review E, vol.79, issue.1, 2009. ,
DOI : 10.1103/PhysRevE.79.016205
-dynamos, Geophysical & Astrophysical Fluid Dynamics, vol.18, issue.1-2, pp.45-57, 2012. ,
DOI : 10.1016/S0031-9201(02)00078-X
URL : https://hal.archives-ouvertes.fr/hal-01175857
Revisiting the ABC flow dynamo, Physics of Fluids, vol.25, issue.3, 2013. ,
DOI : 10.1063/1.4795546
Asymmetric Polarity Reversals, Bimodal Field Distribution, and Coherence Resonance in a Spherically Symmetric Mean-Field Dynamo Model, Physical Review Letters, vol.94, issue.18, 2005. ,
DOI : 10.1103/PhysRevLett.94.184506
On the Optimal Value of the Spectral Abscissa for a System of Linear Oscillators, SIAM Journal on Matrix Analysis and Applications, vol.21, issue.1, pp.195-208, 1999. ,
DOI : 10.1137/S0895479897331850
Stabilization via Nonsmooth, Nonconvex Optimization, IEEE Transactions on Automatic Control, vol.51, issue.11, pp.1760-1769, 2006. ,
DOI : 10.1109/TAC.2006.884944
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.308.1256
A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization, SIAM Journal on Optimization, vol.15, issue.3, pp.751-79, 2005. ,
DOI : 10.1137/030601296
Nonsmooth optimization via quasi-Newton methods, Mathematical Programming, vol.128, issue.1-2, pp.135-63, 2013. ,
DOI : 10.1007/s10107-012-0514-2
URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.365.712
Stability optimization for polynomials and matrices, " in Nonlinear Physical Systems: Spectral Analysis, Stability and Bifurcations, pp.351-75, 2014. ,
Singularities of Caustics and Wave Fronts, Mathematics and Its Applications) Dordrecht: Kluwer, vol.62, 1990. ,
DOI : 10.1007/978-94-011-3330-2
The theory of caustics and wave front singularities with physical applications, Journal of Mathematical Physics, vol.41, issue.6, pp.3344-78, 2000. ,
DOI : 10.1063/1.533316
Lax form of the quantum mechanical eigenvalue problem, Physics Letters A, vol.116, issue.5, pp.227-257, 1986. ,
DOI : 10.1016/0375-9601(86)90138-6
Steepest descent, linear programming, and Hamiltonian flows, Contemp Math, vol.114, pp.77-88, 1990. ,
DOI : 10.1090/conm/114/1097866
Dynamical systems that sort lists, diagonalize matrices, and solve linear programming problems, Linear Algebra and its Applications, vol.146, issue.91, pp.79-91, 1991. ,
DOI : 10.1016/0024-3795(91)90021-N
URL : http://dx.doi.org/10.1016/0024-3795(91)90021-n
Lie-group methods, Acta Numerica 2000, vol.9, issue.0, pp.215-365, 2000. ,
DOI : 10.1017/S0962492900002154
URL : https://hal.archives-ouvertes.fr/hal-01328729
Linear algebra algorithms as dynamical systems, Acta Numerica, vol.17, pp.1-86, 2008. ,
DOI : 10.1017/S0962492906340019
Available online at: http://www.cambridge .org/us/academic/subjects/physics/quantum-physics-quantum-informa tion?and-quantum-computation/non-hermitian-quantum-mechanics, 2011. ,
Exceptional Points in a Microwave Billiard with Time-Reversal Invariance Violation, Physical Review Letters, vol.106, issue.15, 2011. ,
DOI : 10.1103/PhysRevLett.106.150403
Laser-controlled rotational cooling of Na 2 based on exceptional points, Phys Rev A, vol.88, 2013. ,