Stochastic Perturbations to Dynamical Systems: A Response Theory Approach

[1]  Wenlei Wang,et al.  Nonlinearity , 2014, Encyclopedia of Social Network Analysis and Mining.

[2]  Michael Ghil,et al.  Stochastic climate dynamics: Random attractors and time-dependent invariant measures , 2011 .

[3]  Valerio Lucarini,et al.  A statistical mechanical approach for the computation of the climatic response to general forcings , 2010, 1008.0340.

[4]  Juan M López,et al.  Logarithmic bred vectors in spatiotemporal chaos: structure and growth. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Martin Hairer,et al.  A simple framework to justify linear response theory , 2009, Nonlinearity.

[6]  M. Grundmann Kramers–Kronig Relations , 2010 .

[7]  Andrew J. Majda,et al.  Linear response theory for statistical ensembles in complex systems with time-periodic forcing , 2010 .

[8]  Andrew J Majda,et al.  High skill in low-frequency climate response through fluctuation dissipation theorems despite structural instability , 2009, Proceedings of the National Academy of Sciences.

[9]  Yuexin Liu,et al.  Broadband CARS spectral phase retrieval using a time-domain Kramers-Kronig transform. , 2009, Optics letters.

[10]  Andrew J. Majda,et al.  A New Algorithm for Low-Frequency Climate Response , 2009 .

[11]  D. Ruelle A review of linear response theory for general differentiable dynamical systems , 2009, 0901.0484.

[12]  Valerio Lucarini,et al.  Evidence of Dispersion Relations for the Nonlinear Response of the Lorenz 63 System , 2008, 0809.0101.

[13]  A. Vulpiani,et al.  Fluctuation-dissipation: Response theory in statistical physics , 2008, 0803.0719.

[14]  Valerio Lucarini,et al.  Response Theory for Equilibrium and Non-Equilibrium Statistical Mechanics: Causality and Generalized Kramers-Kronig Relations , 2007, 0710.0958.

[15]  Andrew J. Majda,et al.  Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems , 2007 .

[16]  Angelo Vulpiani,et al.  Fluctuation-Response Relation and modeling in systems with fast and slow dynamics , 2007, 0711.1064.

[17]  B. Hunt,et al.  A comparative study of 4D-VAR and a 4D Ensemble Kalman Filter: perfect model simulations with Lorenz-96 , 2007 .

[18]  E. Lorenz Predictability of Weather and Climate: Predictability – a problem partly solved , 2006 .

[19]  V. Lucarini Kramers-Kronig relations in optical materials research , 2005 .

[20]  Edward N. Lorenz,et al.  Designing Chaotic Models , 2005 .

[21]  Anna Trevisan,et al.  Assimilation of Standard and Targeted Observations within the Unstable Subspace of the Observation–Analysis–Forecast Cycle System , 2004 .

[22]  D. Orrell,et al.  Model Error and Predictability over Different Timescales in the Lorenz '96 Systems , 2003 .

[23]  Lai-Sang Young,et al.  What Are SRB Measures, and Which Dynamical Systems Have Them? , 2002 .

[24]  T. Asakura,et al.  Dispersion, Complex Analysis and Optical Spectroscopy , 1999 .

[25]  朝倉 利光,et al.  Dispersion, Complex Analysis and Optical Spectroscopy: Classical Theory , 1998 .

[26]  David Ruelle,et al.  General linear response formula in statistical mechanics, and the fluctuation-dissipation theorem far from equilibrium☆ , 1998 .

[27]  David Ruelle,et al.  Nonequilibrium statistical mechanics near equilibrium: computing higher-order terms , 1998 .

[28]  J. Lindenstrauss,et al.  Classical Banach spaces. I, sequence spaces : reprint of the 1977 edition ; Classical Banach spaces. II, function spaces : reprint of the 1979 edition , 1996 .

[29]  E. Cohen,et al.  Dynamical ensembles in stationary states , 1995, chao-dyn/9501015.

[30]  Donald B. Percival,et al.  Spectral Analysis for Physical Applications , 1993 .

[31]  H. Herzel Chaotic Evolution and Strange Attractors , 1991 .

[32]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[33]  K. Hasselmann Stochastic climate models Part I. Theory , 1976 .

[34]  Joram Lindenstrauss,et al.  Classical Banach spaces , 1973 .

[35]  W. Rudin Real and complex analysis , 1968 .