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.PwMap
RigorousInvariantMeasures.PwMap
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
RigorousInvariantMeasures.ShootingLSV
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.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