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.ApproxInducedLSV
RigorousInvariantMeasures.ApproxInducedLSV
RigorousInvariantMeasures.AverageZero
RigorousInvariantMeasures.CoarseGridQuantities
RigorousInvariantMeasures.ComposedDynamic
RigorousInvariantMeasures.DiscretizedOperator
RigorousInvariantMeasures.DiscretizedOperator
RigorousInvariantMeasures.Dual
RigorousInvariantMeasures.EquispacedPartitionInterval
RigorousInvariantMeasures.FineGridQuantities
RigorousInvariantMeasures.Hat
RigorousInvariantMeasures.Hat
RigorousInvariantMeasures.HatFunction
RigorousInvariantMeasures.HatFunction
RigorousInvariantMeasures.HatFunctionOnTorus
RigorousInvariantMeasures.HatFunctionOnTorus
RigorousInvariantMeasures.IntegralPreservingDiscretizedOperator
RigorousInvariantMeasures.IntervalOnTorus
RigorousInvariantMeasures.MonotonicBranch
RigorousInvariantMeasures.NonIntegralPreservingDiscretizedOperator
RigorousInvariantMeasures.NormCacher
RigorousInvariantMeasures.NormCacher
RigorousInvariantMeasures.Observable
RigorousInvariantMeasures.PwMap
RigorousInvariantMeasures.PwMap
RigorousInvariantMeasures.SymbL
RigorousInvariantMeasures.Ulam
RigorousInvariantMeasures.Ulam
Base.getindex
Base.getindex
Base.getindex
Base.getindex
Base.getindex
Base.iterate
Base.iterate
Base.iterate
Base.iterate
Base.iterate
Base.iterate
Base.iterate
Base.iterate
Base.length
Base.length
Base.length
Base.length
Base.length
Base.length
Base.length
Base.reverse
RecipesBase.apply_recipe
RecipesBase.apply_recipe
RecipesBase.apply_recipe
RecipesBase.apply_recipe
RecipesBase.apply_recipe
RecipesBase.apply_recipe
RigorousInvariantMeasures.Diff
RigorousInvariantMeasures.Diff
RigorousInvariantMeasures.ExtensionOperator
RigorousInvariantMeasures.ShootingLSV
RigorousInvariantMeasures.UniformNoiseUlam2
RigorousInvariantMeasures._eval_T
RigorousInvariantMeasures.abs_or_mag
RigorousInvariantMeasures.add_column!
RigorousInvariantMeasures.aux_normalized_projection_error
RigorousInvariantMeasures.aux_weak_bound
RigorousInvariantMeasures.bound_branch_distortion
RigorousInvariantMeasures.bound_linalg_norm_L1_from_weak
RigorousInvariantMeasures.bound_linalg_norm_L∞_from_weak
RigorousInvariantMeasures.bound_weak_norm_abstract
RigorousInvariantMeasures.bound_weak_norm_from_linalg_norm
RigorousInvariantMeasures.branch
RigorousInvariantMeasures.branch_inverse_derivative
RigorousInvariantMeasures.check_derivatives
RigorousInvariantMeasures.composedPwMap
RigorousInvariantMeasures.compute_coarse_grid_quantities
RigorousInvariantMeasures.compute_fine_grid_quantities
RigorousInvariantMeasures.convergencerateabstract
RigorousInvariantMeasures.dfly
RigorousInvariantMeasures.dfly_inf_der
RigorousInvariantMeasures.discretizationlogder
RigorousInvariantMeasures.distance_from_invariant
RigorousInvariantMeasures.distance_from_invariant_noise
RigorousInvariantMeasures.distortion
RigorousInvariantMeasures.eig_costants_small_matrix
RigorousInvariantMeasures.endpoints
RigorousInvariantMeasures.eval_Clenshaw_BackwardFirst
RigorousInvariantMeasures.evaluate
RigorousInvariantMeasures.evaluate_integral
RigorousInvariantMeasures.finepowernormbounds
RigorousInvariantMeasures.finepowernormboundsnoise
RigorousInvariantMeasures.first_overlapping
RigorousInvariantMeasures.gamma
RigorousInvariantMeasures.get_norm
RigorousInvariantMeasures.get_norm
RigorousInvariantMeasures.has_infinite_derivative_at_endpoints
RigorousInvariantMeasures.has_infinite_derivative_at_endpoints
RigorousInvariantMeasures.infinite_sum_norms
RigorousInvariantMeasures.integral
RigorousInvariantMeasures.integral_covector
RigorousInvariantMeasures.invariant_measure_strong_norm_bound
RigorousInvariantMeasures.invariant_vector
RigorousInvariantMeasures.invariant_vector_noise
RigorousInvariantMeasures.inverse_derivative
RigorousInvariantMeasures.is_integral_preserving
RigorousInvariantMeasures.is_refinement
RigorousInvariantMeasures.last_overlapping
RigorousInvariantMeasures.max_distortion
RigorousInvariantMeasures.max_distortion
RigorousInvariantMeasures.max_inverse_derivative
RigorousInvariantMeasures.max_inverse_derivative
RigorousInvariantMeasures.max_nonzeros_per_row
RigorousInvariantMeasures.mod1_dynamic
RigorousInvariantMeasures.nonzero_on
RigorousInvariantMeasures.nonzero_on
RigorousInvariantMeasures.nonzero_on
RigorousInvariantMeasures.nonzero_on
RigorousInvariantMeasures.normbound
RigorousInvariantMeasures.norms_of_powers
RigorousInvariantMeasures.norms_of_powers_abstract_noise
RigorousInvariantMeasures.norms_of_powers_dfly
RigorousInvariantMeasures.norms_of_powers_from_coarser_grid
RigorousInvariantMeasures.norms_of_powers_from_coarser_grid_noise
RigorousInvariantMeasures.norms_of_powers_noise
RigorousInvariantMeasures.norms_of_powers_trivial
RigorousInvariantMeasures.norms_of_powers_trivial_noise
RigorousInvariantMeasures.one_grid_estimate
RigorousInvariantMeasures.one_vector
RigorousInvariantMeasures.opnormbound
RigorousInvariantMeasures.opnormbound
RigorousInvariantMeasures.plottable
RigorousInvariantMeasures.powernormbounds
RigorousInvariantMeasures.powernormbounds
RigorousInvariantMeasures.preim
RigorousInvariantMeasures.preim
RigorousInvariantMeasures.preimage
RigorousInvariantMeasures.preimage_monotonic
RigorousInvariantMeasures.preimages
RigorousInvariantMeasures.preimages
RigorousInvariantMeasures.preimages_and_derivatives
RigorousInvariantMeasures.range_estimate_monotone
RigorousInvariantMeasures.refine_norms_of_powers
RigorousInvariantMeasures.relative_measure
RigorousInvariantMeasures.residualbound
RigorousInvariantMeasures.residualboundnoise
RigorousInvariantMeasures.restrict
RigorousInvariantMeasures.strong_norm
RigorousInvariantMeasures.strong_weak_bound
RigorousInvariantMeasures.strong_weak_bound
RigorousInvariantMeasures.two_grid_estimate
RigorousInvariantMeasures.unique_increasing
RigorousInvariantMeasures.value_and_derivative
RigorousInvariantMeasures.value_derivative_and_second_derivative
RigorousInvariantMeasures.weak_by_strong_and_aux_bound
RigorousInvariantMeasures.weak_norm
RigorousInvariantMeasures.weak_projection_error
RigorousInvariantMeasures.z_times_conjz
RigorousInvariantMeasures.@define_with_derivatives