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Structure of index sequences for mappings with an asymptotic derivative
On Ulam approximation of the isolated spectrum and eigenfunctions of hyperbolic maps
1. | School of Mathematics and Statistics, University of New South Wales, Sydney NSW 2052, Australia |
[1] |
Stefan Klus, Péter Koltai, Christof Schütte. On the numerical approximation of the Perron-Frobenius and Koopman operator. Journal of Computational Dynamics, 2016, 3 (1) : 51-79. doi: 10.3934/jcd.2016003 |
[2] |
Martin Lustig, Caglar Uyanik. Perron-Frobenius theory and frequency convergence for reducible substitutions. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 355-385. doi: 10.3934/dcds.2017015 |
[3] |
Gary Froyland, Ognjen Stancevic. Escape rates and Perron-Frobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems - B, 2010, 14 (2) : 457-472. doi: 10.3934/dcdsb.2010.14.457 |
[4] |
Marianne Akian, Stéphane Gaubert, Antoine Hochart. A game theory approach to the existence and uniqueness of nonlinear Perron-Frobenius eigenvectors. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 207-231. doi: 10.3934/dcds.2020009 |
[5] |
Gary Froyland, Philip K. Pollett, Robyn M. Stuart. A closing scheme for finding almost-invariant sets in open dynamical systems. Journal of Computational Dynamics, 2014, 1 (1) : 135-162. doi: 10.3934/jcd.2014.1.135 |
[6] |
Stefan Klus, Christof Schütte. Towards tensor-based methods for the numerical approximation of the Perron--Frobenius and Koopman operator. Journal of Computational Dynamics, 2016, 3 (2) : 139-161. doi: 10.3934/jcd.2016007 |
[7] |
Christopher Bose, Rua Murray. The exact rate of approximation in Ulam's method. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 219-235. doi: 10.3934/dcds.2001.7.219 |
[8] |
Jiu Ding, Noah H. Rhee. A unified maximum entropy method via spline functions for Frobenius-Perron operators. Numerical Algebra, Control and Optimization, 2013, 3 (2) : 235-245. doi: 10.3934/naco.2013.3.235 |
[9] |
Hsuan-Wen Su. Finding invariant tori with Poincare's map. Communications on Pure and Applied Analysis, 2008, 7 (2) : 433-443. doi: 10.3934/cpaa.2008.7.433 |
[10] |
Rua Murray. Ulam's method for some non-uniformly expanding maps. Discrete and Continuous Dynamical Systems, 2010, 26 (3) : 1007-1018. doi: 10.3934/dcds.2010.26.1007 |
[11] |
Paweł Góra, Abraham Boyarsky. Stochastic perturbations and Ulam's method for W-shaped maps. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 1937-1944. doi: 10.3934/dcds.2013.33.1937 |
[12] |
Amadeu Delshams, Marian Gidea, Pablo Roldán. Transition map and shadowing lemma for normally hyperbolic invariant manifolds. Discrete and Continuous Dynamical Systems, 2013, 33 (3) : 1089-1112. doi: 10.3934/dcds.2013.33.1089 |
[13] |
Sebastián Ferrer, Francisco Crespo. Alternative angle-based approach to the $\mathcal{KS}$-Map. An interpretation through symmetry and reduction. Journal of Geometric Mechanics, 2018, 10 (3) : 359-372. doi: 10.3934/jgm.2018013 |
[14] |
Vladimir Varlamov. Eigenfunction expansion method and the long-time asymptotics for the damped Boussinesq equation. Discrete and Continuous Dynamical Systems, 2001, 7 (4) : 675-702. doi: 10.3934/dcds.2001.7.675 |
[15] |
Marc Kesseböhmer, Sabrina Kombrink. A complex Ruelle-Perron-Frobenius theorem for infinite Markov shifts with applications to renewal theory. Discrete and Continuous Dynamical Systems - S, 2017, 10 (2) : 335-352. doi: 10.3934/dcdss.2017016 |
[16] |
Gary Froyland, Cecilia González-Tokman, Anthony Quas. Detecting isolated spectrum of transfer and Koopman operators with Fourier analytic tools. Journal of Computational Dynamics, 2014, 1 (2) : 249-278. doi: 10.3934/jcd.2014.1.249 |
[17] |
R. Baier, M. Dellnitz, M. Hessel-von Molo, S. Sertl, I. G. Kevrekidis. The computation of convex invariant sets via Newton's method. Journal of Computational Dynamics, 2014, 1 (1) : 39-69. doi: 10.3934/jcd.2014.1.39 |
[18] |
James W. Cannon, Mark H. Meilstrup, Andreas Zastrow. The period set of a map from the Cantor set to itself. Discrete and Continuous Dynamical Systems, 2013, 33 (7) : 2667-2679. doi: 10.3934/dcds.2013.33.2667 |
[19] |
Huyuan Chen, Feng Zhou. Isolated singularities for elliptic equations with hardy operator and source nonlinearity. Discrete and Continuous Dynamical Systems, 2018, 38 (6) : 2945-2964. doi: 10.3934/dcds.2018126 |
[20] |
Lorenzo Arona, Josep J. Masdemont. Computation of heteroclinic orbits between normally hyperbolic invariant 3-spheres foliated by 2-dimensional invariant Tori in Hill's problem. Conference Publications, 2007, 2007 (Special) : 64-74. doi: 10.3934/proc.2007.2007.64 |
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