RigorousInvariantMeasures.jl
A Julia package which implements a implements a flexible scheme to approximate rigorously invariant measures of dynamical systems.
The package is under active development, with periodic releases.
- Abstract basis
- The Ulam basis
- The hat basis on $S^1$
- The hat basis on $[0,1]$
- The C2 basis
- The Chebyshev basis
- Common Fourier interface
- The Fourier Adjoint basis
- The Fourier Analytic basis
- Abstract Dynamic Definition
- One dimensional piecewise monotone map definition
- Induced Liverani Saussol Vaienti
- Generic assembler
- Generic estimate
- DFLY
- Computing norms of powers
- Norms
- Norm bounds
- Norm Cachers
- Convergence rates abstract operator
- Library
- Differentiation interface
- Background
- Examples
- Implementing a new basis
- RigorousInvariantMeasures.jl
- Userguide
Citing
If you find useful this package, please cite the paper:
Galatolo S., Monge M., Nisoli I., Poloni F. A general framework for the rigorous computation of invariant densities and the coarse-fine strategy [arXiv:2212.05017]
Galatolo S., Nisoli I., An elementary approach to rigorous approximation of invariant measures SIAM J. Appl Dyn Sys.13 pp. 958-985 (2014)
License
RigorousInvariantMeasures is licensed under the MIT license; see LICENSE for the full license text.
Installation
RigorousInvariantMeasures.jl is a registered package, and is simply installed by running
pkg> add("RigorousInvariantMeasures")RigorousInvariantMeasures.ApproxInducedLSVRigorousInvariantMeasures.ApproxInducedLSVRigorousInvariantMeasures.AverageZeroRigorousInvariantMeasures.CoarseGridQuantitiesRigorousInvariantMeasures.ComposedDynamicRigorousInvariantMeasures.DiscretizedOperatorRigorousInvariantMeasures.DiscretizedOperatorRigorousInvariantMeasures.DualRigorousInvariantMeasures.EquispacedPartitionIntervalRigorousInvariantMeasures.FineGridQuantitiesRigorousInvariantMeasures.HatRigorousInvariantMeasures.HatRigorousInvariantMeasures.HatFunctionRigorousInvariantMeasures.HatFunctionRigorousInvariantMeasures.HatFunctionOnTorusRigorousInvariantMeasures.HatFunctionOnTorusRigorousInvariantMeasures.IntegralPreservingDiscretizedOperatorRigorousInvariantMeasures.IntervalOnTorusRigorousInvariantMeasures.MonotonicBranchRigorousInvariantMeasures.NonIntegralPreservingDiscretizedOperatorRigorousInvariantMeasures.NormCacherRigorousInvariantMeasures.NormCacherRigorousInvariantMeasures.ObservableRigorousInvariantMeasures.PwMapRigorousInvariantMeasures.PwMapRigorousInvariantMeasures.SymbLRigorousInvariantMeasures.UlamRigorousInvariantMeasures.UlamBase.getindexBase.getindexBase.getindexBase.getindexBase.getindexBase.iterateBase.iterateBase.iterateBase.iterateBase.iterateBase.iterateBase.iterateBase.iterateBase.lengthBase.lengthBase.lengthBase.lengthBase.lengthBase.lengthBase.lengthBase.reverseRecipesBase.apply_recipeRecipesBase.apply_recipeRecipesBase.apply_recipeRecipesBase.apply_recipeRecipesBase.apply_recipeRecipesBase.apply_recipeRigorousInvariantMeasures.DiffRigorousInvariantMeasures.DiffRigorousInvariantMeasures.ExtensionOperatorRigorousInvariantMeasures.ShootingLSVRigorousInvariantMeasures.UniformNoiseUlam2RigorousInvariantMeasures._eval_TRigorousInvariantMeasures.abs_or_magRigorousInvariantMeasures.add_column!RigorousInvariantMeasures.aux_normalized_projection_errorRigorousInvariantMeasures.aux_weak_boundRigorousInvariantMeasures.bound_branch_distortionRigorousInvariantMeasures.bound_linalg_norm_L1_from_weakRigorousInvariantMeasures.bound_linalg_norm_L∞_from_weakRigorousInvariantMeasures.bound_weak_norm_abstractRigorousInvariantMeasures.bound_weak_norm_from_linalg_normRigorousInvariantMeasures.branchRigorousInvariantMeasures.branch_inverse_derivativeRigorousInvariantMeasures.check_derivativesRigorousInvariantMeasures.composedPwMapRigorousInvariantMeasures.compute_coarse_grid_quantitiesRigorousInvariantMeasures.compute_fine_grid_quantitiesRigorousInvariantMeasures.convergencerateabstractRigorousInvariantMeasures.dflyRigorousInvariantMeasures.dfly_inf_derRigorousInvariantMeasures.discretizationlogderRigorousInvariantMeasures.distance_from_invariantRigorousInvariantMeasures.distance_from_invariant_noiseRigorousInvariantMeasures.distortionRigorousInvariantMeasures.eig_costants_small_matrixRigorousInvariantMeasures.endpointsRigorousInvariantMeasures.eval_Clenshaw_BackwardFirstRigorousInvariantMeasures.evaluateRigorousInvariantMeasures.evaluate_integralRigorousInvariantMeasures.finepowernormboundsRigorousInvariantMeasures.finepowernormboundsnoiseRigorousInvariantMeasures.first_overlappingRigorousInvariantMeasures.gammaRigorousInvariantMeasures.get_normRigorousInvariantMeasures.get_normRigorousInvariantMeasures.has_infinite_derivative_at_endpointsRigorousInvariantMeasures.has_infinite_derivative_at_endpointsRigorousInvariantMeasures.infinite_sum_normsRigorousInvariantMeasures.integralRigorousInvariantMeasures.integral_covectorRigorousInvariantMeasures.invariant_measure_strong_norm_boundRigorousInvariantMeasures.invariant_vectorRigorousInvariantMeasures.invariant_vector_noiseRigorousInvariantMeasures.inverse_derivativeRigorousInvariantMeasures.is_integral_preservingRigorousInvariantMeasures.is_refinementRigorousInvariantMeasures.last_overlappingRigorousInvariantMeasures.max_distortionRigorousInvariantMeasures.max_distortionRigorousInvariantMeasures.max_inverse_derivativeRigorousInvariantMeasures.max_inverse_derivativeRigorousInvariantMeasures.max_nonzeros_per_rowRigorousInvariantMeasures.mod1_dynamicRigorousInvariantMeasures.nonzero_onRigorousInvariantMeasures.nonzero_onRigorousInvariantMeasures.nonzero_onRigorousInvariantMeasures.nonzero_onRigorousInvariantMeasures.normboundRigorousInvariantMeasures.norms_of_powersRigorousInvariantMeasures.norms_of_powers_abstract_noiseRigorousInvariantMeasures.norms_of_powers_dflyRigorousInvariantMeasures.norms_of_powers_from_coarser_gridRigorousInvariantMeasures.norms_of_powers_from_coarser_grid_noiseRigorousInvariantMeasures.norms_of_powers_noiseRigorousInvariantMeasures.norms_of_powers_trivialRigorousInvariantMeasures.norms_of_powers_trivial_noiseRigorousInvariantMeasures.one_grid_estimateRigorousInvariantMeasures.one_vectorRigorousInvariantMeasures.opnormboundRigorousInvariantMeasures.opnormboundRigorousInvariantMeasures.plottableRigorousInvariantMeasures.powernormboundsRigorousInvariantMeasures.powernormboundsRigorousInvariantMeasures.preimRigorousInvariantMeasures.preimRigorousInvariantMeasures.preimageRigorousInvariantMeasures.preimage_monotonicRigorousInvariantMeasures.preimagesRigorousInvariantMeasures.preimagesRigorousInvariantMeasures.preimages_and_derivativesRigorousInvariantMeasures.range_estimate_monotoneRigorousInvariantMeasures.refine_norms_of_powersRigorousInvariantMeasures.relative_measureRigorousInvariantMeasures.residualboundRigorousInvariantMeasures.residualboundnoiseRigorousInvariantMeasures.restrictRigorousInvariantMeasures.strong_normRigorousInvariantMeasures.strong_weak_boundRigorousInvariantMeasures.strong_weak_boundRigorousInvariantMeasures.two_grid_estimateRigorousInvariantMeasures.unique_increasingRigorousInvariantMeasures.value_and_derivativeRigorousInvariantMeasures.value_derivative_and_second_derivativeRigorousInvariantMeasures.weak_by_strong_and_aux_boundRigorousInvariantMeasures.weak_normRigorousInvariantMeasures.weak_projection_errorRigorousInvariantMeasures.z_times_conjzRigorousInvariantMeasures.@define_with_derivatives