Index

• A
• abnormal case 1
• abnormal extremals 1, 2
• absolute endpoint error 1, 2
• absorbed energy 1, 2
• adjoint variables 1
• adjoint-based methods 1
• admissible controlled trajectory 1, 2
• admissible region 1, 2
• admissible trajectory 1
• algebraic potentials 1
• algorithm 1, 2, 3, 4, 5
• Ambrosio and Tortorelli 1
• Ambrosio–Tortorelli approximation 1, 2, 3, 4
• amended frequencymap 1
• amplitude 1
• amplitude distance 1
• angular error 1
• annulus 1, 2
• aperture problem 1, 2
• approximate discontinuity set 1
• Arnold diffusion 1
• Arnold’s normal form 1
• averaging 1
• B
• Baker–Campbell–Hausdorff 1
• Banach spaces 1
• bandlimited 1
• bang–bang control 1
• bang–singular control 1
• Berger sphere 1
• Bessel-functions 1
• BFGS 1, 2
• BFGS algorithm 1
• BFGS iteration 1
• BFGS optimization 1
• biharmonic inpainting 1
• bilevel optimization 1, 2, 3, 4
• bilevel problem 1
• bisystem 1, 2
• Bocop 1
• Bolza problem 1
• boundary conditions 1
• boundary illumination 1, 2
• boundary illumination pattern 1
• bounded eigenvalue property 1
• bounded variation 1
• Bregman distance 1, 2
• Bregman iteration 1, 2, 3
• brightness constancy 1
• Brockett integrator 1, 2
• Brockett system 1
• B-spline 1
• C
• canonical extension 1, 2
• canonical projection 1
• Carathéodory 1
• Cartan flat case 1
• Cartan form 1
• cartoon 1
• cartoon-texture decomposition 1, 2
• Cauchy stress tensor 1
• Cauchy’s inequality 1
• center-unstable foliation 1
• center-unstable manifolds 1
• Chierchia 1
• circle end-point constraint 1
• circular motion 1
• Clarke tangent cone 1
• classical orbital elements 1
• classification 1
• codecs 1, 2
• cohomological equation 1
• compactness theorem 1, 2, 3
• compression 1, 2, 3
• conditional conjugacy 1
• conditional conjugacy theorem 1
• confidence 1
• conjugacy invariant 1
• conjugate time 1, 2
• connecting orbits 1
• constraint qualification 1, 2
• contrast 1
• contrast invariance 1
• control vector field 1
• controllability 1, 2, 3
• controllability criterion 1
• controlled admissible trajectory 1
• controlled Keplerian motion 1
• controlled trajectory 1
• convective regularization 1
• convergence 1, 2, 3
• Γ -convergence 1
• convex 1
• correspondence 1, 2
• cost functional 1
• cotangent bundle 1
• covering map 1
• critical point 1
• cross-correlation 1
• curvature 1
• cut locus 1
• D
• d’Alembert relation 1
• Darboux point 1
• deformation 1, 2
• Delaunay coordinates 1
• denoising 1
• de-orbit problem 1
• Dido problem 1
• diffeomorphic demons 1
• diffeomorphisms 1
• differential field extension 1, 2
• differential form 1
• differential Galois group 1
• differential Galois theory 1
• differential inclusions 1
• diffusion 1, 2, 3
• δ-diffusion orbit 1, 2
• diffusion orbits 1
• diffusion tensor 1
• Diophantine 1, 2
• Diophantine frequency 1
• Diophantine invariant torus 1
• Diophantine tori 1
• Dirac measure 1
• Direct method 1
• Dirichlet boundary 1
• discrepancy term 1
• discretization 1
• discretization points 1
• divergence 1
• drift vector field 1
• dynamic sample size 1
• dynamic sampling 1
• dynamic sampling algorithm 1, 2
• dynamical systems 1
• E
• edge detection 1, 2
• edges 1, 2
• Einstein equation 1
• Einstein metric 1
• Einstein–Weyl geometry 1, 2
• Einstein–Weyl structure 1
• Ekeland’s Theorem 1
• Ekeland’s variational principle 1
• elastic 1
• electric propulsion systems 1
• elliptic functions 1
• elliptic orbits 1
• energy 1
• energy criterion 1
• energy estimate 1
• error measures 1, 2
• essential circle 1
• Euler–Lagrange 1, 2, 3
• Euler–Lagrange inclusion 1
• exact-symplectic diffeomorphisms 1
• extremal 1, 2
• F
• family of minimizers 1
• fast explicit diffusion 1
• fast Fourier transform 1
• FED 1, 2
• feedback group 1
• FFT 1
• fiber-preserving mappings 1
• Filippov Existence Theorem 1
• Filippov theorem 1
• final time 1
• finite element 1, 2
• finite element method (FEM) 1
• first- and second-order necessary optimality conditions 1
• first conjugate point 1
• first integrals 1, 2
• first-order necessary conditions 1
• foliation 1, 2
• four-body problem 1
• free knot 1, 2
• free knot problem 1
• frequency 1
• frequencymap 1, 2, 3, 4
• frequency vector 1
• F -trajectory 1, 2
• fuel-efficient 1
• functional 1, 2, 3
• fundamentalmatrix 1, 2
• G
• Galois group 1
• Gauss curvature 1
• Gaussian 1, 2, 3
• Gaussian noise 1
• generalized ball 1
• geodesics 1
• geometry 1
• germs 1
• germs of integrable potentials 1
• G-invariant KAM theorem 1
• gradient 1, 2, 3
• grand resistance matrix 1
• Gronwall’s Lemma 1
• group 1
• group action 1
• Grüneisen coefficient 1, 2
• H
• Hadamard inequalities 1
• Hadamard interpolation inequalities 1
• Hamiltonian 1, 2, 3, 4, 5, 6, 7
• Hamiltonian flow 1
• Hamiltonian function 1
• Hamiltonian lifts 1
• Hamiltonian methods 1
• Hamiltonian system 1
• HamPath 1
• harmonic 1, 2, 3
• Heisenberg group 1, 2, 3
• higher variational equations 1, 2
• Hilbert dimension 1
• homoclinic intersection 1
• homoclinic map 1
• homogeneous potential 1
• Horn–Schunck 1
• Huber function 1
• Huber regularization 1, 2
• hyperbolic annulus 1, 2
• hyperbolic inclination 1
• hyperbolic manifolds 1
• hyperbolic orbit 1
• hyperbolic persistence 1
• hyperbolic shadowing 1
• hyperbolic torus 1
• hypertangent vector 1
• I
• image compression 1
• image sequence 1
• implicit state constraints 1
• impulse 1, 2
• impulse noise 1
• indirect method 1
• inf-convolution 1
• infimal-convolution total variation 1
• initial mass 1
• initial pressure 1
• initial state 1
• initial value 1
• initialization 1, 2, 3, 4
• initialization guess 1
• inpainting 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
• integrability 1
• integrability condition 1
• integrable 1, 2
• interface conditions 1, 2
• interior-point method 1
• interpolation 1
• interpolation inequalities 1
• invariance 1, 2
• invariant 1, 2, 3
• invariant annulus 1
• invariant tensors 1
• invariant torus 1, 2
• invariant torus theorem 1
• inverse 1
• inverse function theorem 1
• inward pointing condition 1
• isochronic 1
• isocost extremals 1
• isoenergetic 1
• isoenergetic theorem 1
• iterative scheme 1
• J
• Jacobi coordinates 1
• Jacobian 1
• K
• KAM theory 1, 2, 3
• Kantorovich–Rubinstein norm 1
• Keplerian frequencymap 1
• Keplerian motion 1, 2, 3
• knot distribution 1, 2
• Kolmogorov 1
• Kovacic algorithm 1
• L
• L1-TV model 1
• L1-TV/L2 model 1
• L1-TV/TV 1
• L1-TV/TVmodel 1
• landmark 1, 2
• Laplacian 1
• large-scale flow 1
• large-scale motion 1
• L-curve 1
• LDDMM 1
• learning pipeline 1
• Lebesgue-measurable 1
• Levi–Civita connection 1
• Liapunov exponents 1
• Lie bracket 1
• Lie group 1
• lifted map 1
• limiting normal cone 1
• limiting value 1
• Lindstedt normal form 1
• linear system 1
• linearized equation 1
• linearized operator 1
• linearized problem 1, 2
• linearized system 1, 2
• Liouville canonical one-form 1
• Liouville integrable 1
• Lipschitz 1
• Lipschitz curve 1
• Lipschitz regularity 1
• local inverse 1
• local system 1
• Lorentzian signature 1
• low thrust 1
• lower dimensional tori 1
• lower semicontinuous 1
• low-thrust control 1
• M
• Magnetic Resonance Imaging (MRI) 1
• mask 1, 2, 3, 4
• mass center 1
• mathematical programs with equilibrium constraints 1
• maximal trajectory 1
• Maximum A Posteriori (MAP) approach 1
• maximum principle 1, 2, 3
• maximum thrust 1
• mean image 1
• measurement operator 1
• Melnikov condition 1
• metric 1, 2
• Metropolis Hastings 1
• Meyer space 1
• micro-swimmers 1, 2
• minimal time 1
• minimal time problem 1
• minimization 1
• minimizer 1, 2, 3
• minimum description length 1
• minimum time problem 1
• MNIST 1
• model 1
• modified equinoctial orbital elements 1
• Moeckel’s method 1
• moments 1
• monomials 1
• Morales–Ramis theorem 1
• Morales–Ramis–Simo 1
• motion estimation 1, 2, 3, 4, 5, 6, 7
• MPEC 1
• MRI 1
• multi-illumination 1
• multiplier 1, 2
• multiscale 1
• Mumford–Shah 1, 2, 3
• Mumford–Shah functional 1, 2
• Mumford–Shah-like functional 1
• mutual information 1
• N
• Nash–Moser theorem 1
• N-body problem 1
• necessary conditions 1, 2
• Neumann boundary conditions 1
• Newton algorithm 1, 2
• Newton laws 1
• nilpotent approximation 1
• noise 1, 2, 3
• nondegeneracy condition 1, 2
• nonlinear equation 1
• nonlinear minimization problem 1
• nonlocal 1, 2
• non-local means 1
• nonresonant vector 1
• nonsmooth PDE-constraints 1
• nonunique minimizers 1
• normal case 1, 2
• normal form 1, 2
• normal hyperbolicity 1
• normalization condition 1
• normalized coordinates 1
• not integrable 1, 2
• numerical examples 1
• numerical method 1, 2
• O
• objective function 1
• of 1
• optical absorption coefficient 1
• optical flow 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11
• optical flow constraint 1, 2
• optimal control 1
• optimal control problem 1, 2
• optimal deformation 1, 2
• optimal exponent 1
• optimal final time 1
• optimal knot 1
• optimal regularization parameters 1
• optimal tonal data 1
• optimal trajectory 1, 2, 3
• optimality conditions 1
• optimization 1
• optimization problem 1, 2
• optimized 1
• orbital manoeuvring system 1
• orbital transfer problem 1
• orthogonal projection 1
• oscillating case 1
• P
• parallelizable 1
• parallelized 1
• parameters 1, 2
• parametrization 1
• parametrization approach 1
• partial differential equation 1
• patch 1
• PatchMatch 1, 2
• PDE 1, 2
• PDE constraints 1
• PDE-constrained optimization 1
• penalization argument 1
• period 1
• periodic end-point constraints 1
• periodic optimal controls 1
• periodic orbit 1
• periodic region 1
• periodic trajectory 1
• persistence of tori 1
• perturbation 1, 2
• perturbed diffeomorphism 1
• phase 1, 2
• phase portrait 1
• photoacoustic tomography 1
• Poincaré coordinates 1
• Poincaré recurrence theorem 1
• point mask 1
• Poisson 1, 2, 3
• Poisson brackets 1
• Poisson noise 1, 2, 3, 4
• polar coordinates 1
• polynomial function 1
• Pontryagin maximum principle 1, 2, 3
• Positron Emission Tomography (PET) 1
• primal–dual algorithm 1, 2
• primal–dual Newton-type algorithm 1
• primitive functions 1
• privileged coordinates 1
• probabilistic sparsification 1
• probability density 1
• projected orbits 1
• pseudo-Hamiltonian 1
• Purcell swimmer 1
• Q
• quadrupolar frequencymap 1
• quadrupolar system 1
• quantification 1, 2, 3
• quasi-Newton algorithm 1
• quasiperiodic flows 1
• quasiperiodic solutions 1
• quasiperiodic time-dependent perturbations 1
• quasi-static Newton law 1
• R
• radiative transfer equation 1
• rank condition 1
• rational potential 1
• rationally parametrizable 1
• recognition 1
• reconstruction 1
• recurrent points 1
• Reeb vector field 1, 2
• reference arc 1
• reference cost 1
• reference trajectory 1
• registration 1, 2, 3
• regularity conditions 1
• regularization 1, 2, 3, 4
• regularization term 1
• regularizer 1, 2
• remainder 1
• resistive force theory 1
• resonance points 1
• resonance zones 1
• restoration 1
• Ricci curvature 1
• Ricci tensor 1
• Riemann curvature tensor 1
• Riemannian geometry 1
• Riemannian signature 1
• right inverse 1
• rotation 1
• Rüssmann 1, 2
• S
• sampling 1, 2, 3
• scale-space 1
• Schwarz domain decomposition 1
• second-order approximation 1
• second-order conditions 1, 2
• second-order optimality conditions 1
• second-order sufficient 1
• second-order sufficient conditions 1
• second-order TGV 1
• second-order total generalized variation 1
• second-order total variation 1, 2
• second-order TV regularization 1
• sectional curvature 1
• semismooth Newton 1, 2
• semismooth Newton approach 1
• sensitivity 1, 2, 3, 4
• series expansion 1
• set of tori 1
• shooting method 1
• SIFT 1
• signal-to-noise ratio (SNR) 1
• single-input affine system 1
• singular control 1
• smoothing 1
• smoothness 1
• solution 1-NOSE 2
• source condition 1
• sparse inpainting 1
• sparsification 1, 2
• spatial and tonal data optimization 1
• spatial data 1, 2
• spatial optimization 1
• spatial pendulum 1
• special function of bounded variation 1, 2, 3
• spectrum 1
• spline 1
• stable periodic region 1
• state arc 1
• state constraint 1, 2, 3
• state variable 1
• state-constrained 1
• state-local optimality 1
• stationary point 1
• statistical analysis 1
• steerability 1
• steganographic 1
• stochastic approximation 1
• stochastic sparsification 1
• Stokes equation 1
• Stokes theorem 1
• strong local minimizer 1
• strong local minimum 1, 2
• strong minimizer 1
• structural functions 1, 2
• structure group 1
• structures 1
• subgradient 1
• sub-Lorentzian 1, 2
• sub-pseudo-Riemannian structure 1
• sub-pseudo-Riemannian symmetries 1
• sub-Riemannian 1
• sub-Riemannian case 1
• sub-Riemannianmanifold 1
• sufficient condition 1, 2
• sufficient optimality conditions 1
• super-Hamiltonian 1
• super-resolution 1
• supervised learning 1
• SURE estimator 1
• surrogate 1
• swimmer 1
• symmetry 1
• symplectic constraint 1
• symplectic embedding 1, 2
• symplectic manifold 1
• symplectic operator 1
• symplectic structure 1
• symplectomorphism 1
• T
• texture 1, 2, 3, 4, 5
• the smallest period 1
• three-body problem 1, 2
• Tikhonov regularization 1
• time- and space-oriented 1
• time-optimal 1
• time-optimal controllability 1
• time-optimal trajectory 1
• tonal 1
• tonal data 1, 2
• tonal data optimization 1
• tonal optimization 1, 2
• Tonelli Hamiltonian 1
• Total Generalized Variation 1, 2
• total variation 1, 2, 3, 4, 5, 6, 7, 8, 9
• total variation regularization 1
• transcendental cases 1
• transcendental coefficients 1
• transversality condition 1, 2, 3, 4, 5
• TV regularization 1
• TV-L2 1
• twist map 1, 2
• twisted conjugacy 1, 2
• two-step optimization 1
• U
• ultrasound pressure wave 1
• unconstrained 1
• unprescribed frequencies 1
• unstable periodic region 1
• V
• variational 1, 2
• variational equation 1, 2, 3, 4
• variational method 1, 2
• vector field 1
• velocity 1
• velocity set 1
• video 1
• W
• W1,1 δ-local minimizer 1
• W1,1-local minimizer 1
• warping 1
• waves 1
• Whitney 1
• Whitney-smoothness 1
• Z
• Ziglin lemma 1
• zooming 1

Radon Series on Computational and Applied Mathematics

Volume 16

Harald Niederreiter, Alina Ostafe, Daniel Panario, Arne Winterhof (Eds.), 2014

Algebraic Curves and Finite Fields. Cryptography and Other Applications

ISBN: 978-3-11-031788-6, e-ISBN: 978-3-11-031791-6, ISSN: 1865-3707

Volume 15

Peter Kritzer, Harald Niederreiter, Friedrich Pillichshammer, Arne Winterhof (Eds.),2014

Uniform Distribution and Quasi-Monte Carlo Methods. Discrepancy, Integration andApplications

ISBN: 978-3-11-031789-3, e-ISBN: 978-3-11-031793-0, ISSN: 1865-3707

Volume 14

Ivan G. Graham, Ulrich Langer, Jens M. Melenk, Mourad Sini (Eds.), 2013

Direct and Inverse Problems in Wave Propagation and Applications

ISBN: 978-3-11-028223-8, eISBN: 978-3-11-028228-3, ISSN: 1865-3707

Volume 13

Mike Cullen, Melina A Freitag, Stefan Kindermann, Robert Scheichl (Eds.), 2013

Large Scale Inverse Problems. Computational Methods and Applications in the EarthSciences

ISBN: 978-3-11-028223-8, eISBN: 978-3-11-028228-3, ISSN: 1865-3707

Volume 12

Peter Bastian, Johannes Kraus, Robert Scheichl, Mary Wheeler (Eds.), 2013

Simulation of Flow in Porous Media. Applications in Energy and Environment

ISBN 978-3-11-028221-4, e-ISBN 978-3-11-028224-5, Set-ISBN 978-3-11-028225-2

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Pascale Charpin, Alexander Pott, Arne Winterhof (Eds.), 2013

Finite Fields and Their Applications

ISBN 978-3-11-028240-5, e-ISBN 978-3-11-028360-0, Set-ISBN 978-3-11-028361-7