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Saddlenode bifurcation of homoclinic orbits in singular systems
The exact rate of approximation in Ulam's method
1.  Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045, Victoria, BC, Canada V8W 3P4, Canada 
2.  Department of Mathematics, University of Waikato, Private Bag 3105, Hamilton, New Zealand 
[1] 
Stefan Klus, Péter Koltai, Christof Schütte. On the numerical approximation of the PerronFrobenius and Koopman operator. Journal of Computational Dynamics, 2016, 3 (1) : 5179. doi: 10.3934/jcd.2016003 
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Martin Lustig, Caglar Uyanik. PerronFrobenius theory and frequency convergence for reducible substitutions. Discrete and Continuous Dynamical Systems, 2017, 37 (1) : 355385. doi: 10.3934/dcds.2017015 
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Gary Froyland, Ognjen Stancevic. Escape rates and PerronFrobenius operators: Open and closed dynamical systems. Discrete and Continuous Dynamical Systems  B, 2010, 14 (2) : 457472. doi: 10.3934/dcdsb.2010.14.457 
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Marianne Akian, Stéphane Gaubert, Antoine Hochart. A game theory approach to the existence and uniqueness of nonlinear PerronFrobenius eigenvectors. Discrete and Continuous Dynamical Systems, 2020, 40 (1) : 207231. doi: 10.3934/dcds.2020009 
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Fanni M. Sélley. A selfconsistent dynamical system with multiple absolutely continuous invariant measures. Journal of Computational Dynamics, 2021, 8 (1) : 932. doi: 10.3934/jcd.2021002 
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Simon Lloyd, Edson Vargas. Critical covering maps without absolutely continuous invariant probability measure. Discrete and Continuous Dynamical Systems, 2019, 39 (5) : 23932412. doi: 10.3934/dcds.2019101 
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Stefan Klus, Christof Schütte. Towards tensorbased methods for the numerical approximation of the PerronFrobenius and Koopman operator. Journal of Computational Dynamics, 2016, 3 (2) : 139161. doi: 10.3934/jcd.2016007 
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Jiu Ding, Aihui Zhou. Absolutely continuous invariant measures for piecewise $C^2$ and expanding mappings in higher dimensions. Discrete and Continuous Dynamical Systems, 2000, 6 (2) : 451458. doi: 10.3934/dcds.2000.6.451 
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Jawad AlKhal, Henk Bruin, Michael Jakobson. New examples of Sunimodal maps with a sigmafinite absolutely continuous invariant measure. Discrete and Continuous Dynamical Systems, 2008, 22 (1&2) : 3561. doi: 10.3934/dcds.2008.22.35 
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Lucia D. Simonelli. Absolutely continuous spectrum for parabolic flows/maps. Discrete and Continuous Dynamical Systems, 2018, 38 (1) : 263292. doi: 10.3934/dcds.2018013 
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Rua Murray. Approximation error for invariant density calculations. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 535557. doi: 10.3934/dcds.1998.4.535 
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Arno Berger, Roland Zweimüller. Invariant measures for general induced maps and towers. Discrete and Continuous Dynamical Systems, 2013, 33 (9) : 38853901. doi: 10.3934/dcds.2013.33.3885 
[13] 
Xavier Bressaud. Expanding interval maps with intermittent behaviour, physical measures and time scales. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 517546. doi: 10.3934/dcds.2004.11.517 
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Adrian Tudorascu. On absolutely continuous curves of probabilities on the line. Discrete and Continuous Dynamical Systems, 2019, 39 (9) : 51055124. doi: 10.3934/dcds.2019207 
[15] 
Leandro Cioletti, Artur O. Lopes, Manuel Stadlbauer. Ruelle operator for continuous potentials and DLRGibbs measures. Discrete and Continuous Dynamical Systems, 2020, 40 (8) : 46254652. doi: 10.3934/dcds.2020195 
[16] 
Fawwaz Batayneh, Cecilia GonzálezTokman. On the number of invariant measures for random expanding maps in higher dimensions. Discrete and Continuous Dynamical Systems, 2021, 41 (12) : 58875914. doi: 10.3934/dcds.2021100 
[17] 
Christoph Bandt, Helena PeÑa. Polynomial approximation of selfsimilar measures and the spectrum of the transfer operator. Discrete and Continuous Dynamical Systems, 2017, 37 (9) : 46114623. doi: 10.3934/dcds.2017198 
[18] 
Tatsuya Arai, Naotsugu Chinen. The construction of chaotic maps in the sense of Devaney on dendrites which commute to continuous maps on the unit interval. Discrete and Continuous Dynamical Systems, 2004, 11 (2&3) : 547556. doi: 10.3934/dcds.2004.11.547 
[19] 
Chengxiang Wang, Li Zeng. Error bounds and stability in the $l_{0}$ regularized for CT reconstruction from small projections. Inverse Problems and Imaging, 2016, 10 (3) : 829853. doi: 10.3934/ipi.2016023 
[20] 
Walter Alt, Robert Baier, Matthias Gerdts, Frank Lempio. Error bounds for Euler approximation of linearquadratic control problems with bangbang solutions. Numerical Algebra, Control and Optimization, 2012, 2 (3) : 547570. doi: 10.3934/naco.2012.2.547 
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