L. Nicoud, C. Benoit, T. Sensiau, and . Poinsot, Acoustic Modes in Combustors with Complex Impedances and Multidimensional Active Flames, AIAA Journal, vol.45, issue.2, pp.426-441, 2007.
DOI : 10.2514/1.24933
URL : https://hal.archives-ouvertes.fr/hal-00908192

R. I. Balasubramanian and . Sujith, Thermoacoustic instability in a Rijke tube: Non-normality and nonlinearity, Physics of Fluids, vol.20, issue.4, pp.44103-44104, 2008.
DOI : 10.1063/1.2895634

N. Trefethen, A. E. Trefethen, S. C. Reddy, and T. A. Driscoll, Hydrodynamic Stability Without Eigenvalues, Science, vol.261, issue.5121, pp.578-584, 1993.
DOI : 10.1126/science.261.5121.578

P. Henningson and . Schmid, Vector eigenfunction expansions for plane channel flows, Stud. Appl. Math, vol.87, 1992.

J. Schmid and D. S. Henningson, Stability and Transition in Shear Flows, 2001.
DOI : 10.1007/978-1-4613-0185-1

J. Lim and . Kim, A singular value analysis of boundary layer control, Physics of Fluids, vol.16, issue.6, p.16, 2004.
DOI : 10.1063/1.1710522

E. C. Culick, Combustion instabilities in liquid-fueled propulsion systems -An overview, AGARD Conference Proceedings No. 450, 72B Specialists' Meeting of the AGARD Propulsion and Energetics Panel, 1988.

K. Nagaraja, R. I. Kedia, and . Sujith, Characterizing energy growth during combustion instabilities: Singularvalues or eigenvalues?, Proceedings of the Combustion Institute, vol.32, issue.2, pp.2933-2940, 2009.
DOI : 10.1016/j.proci.2008.05.035

K. Nicoud and . Wieczorek, About the zero Mach number assumption in the calculation of thermoacoustic instabilities, International Journal of Spray and Combustion Dynamics, vol.142, issue.7, pp.67-112, 2009.
DOI : 10.1260/175682709788083335
URL : https://hal.archives-ouvertes.fr/hal-00803826

. Landau, On Szeg?????s eingenvalue distribution theorem and non-Hermitian kernels, Journal d'Analyse Math??matique, vol.206, issue.1, pp.335-357, 1975.
DOI : 10.1007/BF02786820

N. Trefethen, Computation of pseudospectra, Acta Numerica, vol.I, pp.247-295, 1999.
DOI : 10.1016/0167-6911(93)90115-M

F. Sensiau, T. Nicoud, and . Poinsot, A Tool to Study Azimuthal Standing and Spinning Modes in Annular Combustors, International Journal of Aeroacoustics, vol.142, issue.4, pp.57-68, 2009.
DOI : 10.1260/147547209786235037
URL : https://hal.archives-ouvertes.fr/hal-00803828

S. Gullaud, C. Mendez, F. Sensiau, T. Nicoud, and . Poinsot, Effect of multiperforated plates on the acoustic modes in combustors, Comptes Rendus M??canique, vol.337, issue.6-7, pp.406-414, 2009.
DOI : 10.1016/j.crme.2009.06.020
URL : https://hal.archives-ouvertes.fr/hal-00803809

P. Dowling, The calculation of thermoacoustic oscillations, Journal of Sound and Vibration, vol.180, issue.4, pp.557-581, 1995.
DOI : 10.1006/jsvi.1995.0100

S. Gebhardt and . Grossmann, Chaos transition despite linear stability, Physical Review E, vol.50, issue.5, p.3705, 1994.
DOI : 10.1103/PhysRevE.50.3705

R. Mariappan and . Sujith, Thermoacoustic instability in a solid rocket motor: non-normality and nonlinear instabilities, Journal of Fluid Mechanics, vol.90, pp.1-33, 2010.
DOI : 10.1002/1097-0363(20000715)33:5<627::AID-FLD931>3.0.CO;2-A

T. Lieuwen and V. Yang, Combustion Instabilities in Gas Turbine Engines. Operational Experience, Fundamental Mechanisms and Modeling, Prog. in Astronautics and AeronauticsAIAA, 2005.

. Crocco, Aspects of Combustion Stability in Liquid Propellant Rocket Motors Part I: Fundamentals. Low Frequency Instability With Monopropellants, Journal of the American Rocket Society, vol.21, issue.6, pp.163-178, 1951.
DOI : 10.2514/8.4393

. Crocco, Aspects of Combustion Stability in Liquid Propellant Rocket Motors Part II: Low Frequency Instability with Bipropellants. High Frequency Instability, Journal of the American Rocket Society, vol.22, issue.1, pp.7-16, 1952.
DOI : 10.2514/8.4410

D. Noiray, T. Durox, S. Schuller, and . Candel, A unified framework for nonlinear combustion instability analysis based on the flame describing function, Journal of Fluid Mechanics, vol.21, pp.139-167, 2008.
DOI : 10.1016/j.proci.2006.07.096

K. Myers, Transport of energy by disturbances in arbitrary steady flows J. Fluid with heat communication, J. Fluid Mech, vol.597, pp.67-89, 2008.

T. Giauque, M. Poinsot, F. Brear, and . Nicoud, Budget of disturbance energy in gaseous reacting flows, Proc. of the Summer Program (Center for Turbulence Research, pp.285-297, 2006.

C. O. Polifke, K. Paschereit, and . Döbbeling, Constructive and Destructive Interference of Acoustic and Entropy Waves in a Premixed Combustor with a Choked Exit, The International Journal of Acoustics and Vibration, vol.6, issue.3, pp.135-146, 2001.
DOI : 10.20855/ijav.2001.6.382

E. Marble and S. Candel, Acoustic disturbance from gas non-uniformities convected through a nozzle, Journal of Sound and Vibration, vol.55, issue.2, pp.225-243, 1977.
DOI : 10.1016/0022-460X(77)90596-X

F. Nicoud and T. Poinsot, Thermoacoustic instabilities: Should the Rayleigh criterion be extended to include entropy changes?, Combustion and Flame, vol.142, issue.1-2, pp.153-159, 2005.
DOI : 10.1016/j.combustflame.2005.02.013
URL : https://hal.archives-ouvertes.fr/hal-00908285

P. Mariappan, R. Schmid, and . Sujith, Role of transient growth in subcritical transition to thermoacoustic instablitiy in a horizontal Rijke tube, 16th AIAA/CEAS Aeroacoustics Conference, pp.2010-3857, 2010.

P. Subramanian and R. Sujith, Non-normality and internal flame dynamics in premixed flame???acoustic interaction, Journal of Fluid Mechanics, vol.679, pp.315-342, 2011.
DOI : 10.1017/jfm.2011.140