Skip to main content
U.S. Department of Energy
Office of Scientific and Technical Information

Efficient Computation of Linear Response of Chaotic Attractors with One-Dimensional Unstable Manifolds

Journal Article · · SIAM Journal on Applied Dynamical Systems
DOI:https://doi.org/10.1137/21m1405599· OSTI ID:1980772

Not provided.

Research Organization:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Organization:
USDOE National Nuclear Security Administration (NNSA)
DOE Contract Number:
NA0003993
OSTI ID:
1980772
Journal Information:
SIAM Journal on Applied Dynamical Systems, Vol. 21, Issue 2; ISSN 1536-0040
Publisher:
Society for Industrial and Applied Mathematics (SIAM)
Country of Publication:
United States
Language:
English

References (50)

Blended response algorithms for linear fluctuation-dissipation for complex nonlinear dynamical systems journal October 2007
Extreme Sensitivity and Climate Tipping Points journal November 2019
A rigorous computational approach to linear response journal February 2018
Linear response in the intermittent family: Differentiation in a weighted $C^0$-norm journal October 2016
Linear response for smooth deformations of generic nonuniformly hyperbolic unimodal maps journal January 2012
Linear Response for Intermittent Maps journal February 2016
Adjoint sensitivity analysis of chaotic dynamical systems with non-intrusive least squares shadowing journal November 2017
Are extreme dissipation events predictable in turbulent fluid flows? journal April 2019
Can we use linear response theory to assess geoengineering strategies? journal February 2020
Differentiability of thermodynamical quantities in non-uniformly expanding dynamics journal April 2016
Lyapunov analysis: from dynamical systems theory to applications journal June 2013
Linear response in neuronal networks: From neurons dynamics to collective response journal October 2019
An ergodic-averaging method to differentiate covariant Lyapunov vectors: Computing the curvature of one-dimensional unstable manifolds of strange attractors journal May 2021
On the probability of finding nonphysical solutions through shadowing journal September 2021
Least Squares Shadowing Method for Sensitivity Analysis of Differential Equations journal January 2017
Rough parameter dependence in climate models and the role of Ruelle-Pollicott resonances journal January 2014
Limit theorems and Markov approximations for chaotic dynamical systems journal September 1995
Projected Shadowing-Based Data Assimilation journal January 2018
Approximation by Brownian motion for Gibbs measures and flows under a function journal December 1984
On differentiability of SRB states for partially hyperbolic systems journal February 2004
Ruelle's linear response formula, ensemble adjoint schemes and Lévy flights journal July 2004
A linear response for dynamical systems with additive noise journal May 2019
Covariant Lyapunov vectors journal June 2013
Compact locally maximal hyperbolic sets for smooth maps: fine statistical properties journal July 2008
A simple framework to justify linear response theory journal March 2010
Prevalence of non-Lipschitz Anosov foliations journal June 1999
Sensitivity Analysis of Chaotic Systems Using Unstable Periodic Orbits journal January 2018
Sensitivity analysis of the climate of a chaotic system journal January 2000
The Metric Entropy of Diffeomorphisms: Part I: Characterization of Measures Satisfying Pesin's Entropy Formula journal November 1985
Stochastic Perturbations to Dynamical Systems: A Response Theory Approach journal January 2012
Transitions across Melancholia States in a Climate Model: Reconciling the Deterministic and Stochastic Points of View journal April 2019
A vector-valued almost sure invariance principle for hyperbolic dynamical systems journal March 2009
Hyperbolicity, shadowing directions and sensitivity analysis of a turbulent three-dimensional flow journal January 2019
Adjoint sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Adjoint Shadowing (NILSAS) journal October 2019
Sensitivity analysis on chaotic dynamical systems by Non-Intrusive Least Squares Shadowing (NILSS) journal October 2017
Hölder foliations journal January 1997
Effects of Periodic Forcing on a Paleoclimate Delay Model journal January 2019
A new framework for climate sensitivity and prediction: a modelling perspective journal May 2015
Differentiation of SRB States journal July 1997
Differentiation of SRB States: Correction and Complements journal March 2003
Differentiation of SRB states for hyperbolic flows journal April 2008
A review of linear response theory for general differentiable dynamical systems journal March 2009
Ergodic sensitivity analysis of one-dimensional chaotic maps journal November 2020
Computational assessment of smooth and rough parameter dependence of statistics in chaotic dynamical systems journal October 2021
Unsteady Adjoint of Pressure Loss for a Fundamental Transonic Turbine Vane journal November 2016
Convergence of the Least Squares Shadowing Method for Computing Derivative of Ergodic Averages journal January 2014
On the Validity of Linear Response Theory in High-Dimensional Deterministic Dynamical Systems journal July 2018
Linear response for macroscopic observables in high-dimensional systems journal November 2019
Statistical Properties of Dynamical Systems with Some Hyperbolicity journal May 1998
What Are SRB Measures, and Which Dynamical Systems Have Them? journal January 2002