Yamaguchi, Yoshihiro; Tanikawa, Kiyotaka Proof of the transverse intersection of the stable and unstable manifolds in the two-dimensional area preserving map. (English) Zbl 07711712 PTEP, Prog. Theor. Exper. Phys. 2023, No. 5, Article ID 053A01, 11 p. (2023). MSC: 37E20 37E40 37C25 PDF BibTeX XML Cite \textit{Y. Yamaguchi} and \textit{K. Tanikawa}, PTEP, Prog. Theor. Exper. Phys. 2023, No. 5, Article ID 053A01, 11 p. (2023; Zbl 07711712) Full Text: DOI
Chen, Lei; Markovic, Vladimir Non-realizability of the Torelli group as area-preserving homeomorphisms. (English) Zbl 1471.37049 J. Lond. Math. Soc., II. Ser. 102, No. 3, 957-976 (2020). Reviewer: Alireza Najafizadeh (Tabriz) MSC: 37E30 37E10 37E40 20K15 20K20 PDF BibTeX XML Cite \textit{L. Chen} and \textit{V. Markovic}, J. Lond. Math. Soc., II. Ser. 102, No. 3, 957--976 (2020; Zbl 1471.37049) Full Text: DOI arXiv
Mugnaine, Michele; Batista, Antonio M.; Caldas, Iberê L.; Szezech, José D. jun.; Viana, Ricardo L. Ratchet current in nontwist Hamiltonian systems. (English) Zbl 1458.37057 Chaos 30, No. 9, 093141, 9 p. (2020). Reviewer: William J. Satzer Jr. (St. Paul) MSC: 37E40 37A05 37C25 PDF BibTeX XML Cite \textit{M. Mugnaine} et al., Chaos 30, No. 9, 093141, 9 p. (2020; Zbl 1458.37057) Full Text: DOI
Matheus, Carlos On the dynamics on the \(\mathrm{SU}(2)\)-character variety of a once-punctured torus. (English) Zbl 1510.37076 Actes de séminaire de théorie spectrale et géométrie. Année 2017–2019. St. Martin d’Hères: Université de Grenoble I, Institut Fourier. Sémin. Théor. Spectr. Géom. 35, 109-119 (2019). MSC: 37E40 37J40 PDF BibTeX XML Cite \textit{C. Matheus}, Sémin. Théor. Spectr. Géom. 35, 109--119 (2019; Zbl 1510.37076) Full Text: DOI
Qin, Wen-Xin; Wang, Ya-Nan Invariant circles and depinning transition. (English) Zbl 1390.37075 Ergodic Theory Dyn. Syst. 38, No. 2, 761-787 (2018). MSC: 37E40 37J45 PDF BibTeX XML Cite \textit{W.-X. Qin} and \textit{Y.-N. Wang}, Ergodic Theory Dyn. Syst. 38, No. 2, 761--787 (2018; Zbl 1390.37075) Full Text: DOI
Pelayo, Álvaro; Rezakhanlou, Fraydoun Poincaré-Birkhoff theorems in random dynamics. (English) Zbl 1433.37004 Trans. Am. Math. Soc. 370, No. 1, 601-639 (2018). MSC: 37A30 37A05 37E40 PDF BibTeX XML Cite \textit{Á. Pelayo} and \textit{F. Rezakhanlou}, Trans. Am. Math. Soc. 370, No. 1, 601--639 (2018; Zbl 1433.37004) Full Text: DOI arXiv
Denette, Erin; Kulenović, Mustafa R. S.; Pilav, Esmir Birkhoff normal forms, KAM theory and time reversal symmetry for certain rational map. (English) Zbl 1344.37068 Mathematics 4, No. 1, Paper No. 20, 12 p. (2016). MSC: 37J40 37E40 39A28 39A30 39A23 37M05 PDF BibTeX XML Cite \textit{E. Denette} et al., Mathematics 4, No. 1, Paper No. 20, 12 p. (2016; Zbl 1344.37068) Full Text: DOI
Gaidashev, Denis; Johnson, Tomas Spectral properties of renormalization for area-preserving maps. (English) Zbl 1354.37046 Discrete Contin. Dyn. Syst. 36, No. 7, 3651-3675 (2016). MSC: 37E20 37E40 37D25 37A05 37C15 37J10 PDF BibTeX XML Cite \textit{D. Gaidashev} and \textit{T. Johnson}, Discrete Contin. Dyn. Syst. 36, No. 7, 3651--3675 (2016; Zbl 1354.37046) Full Text: DOI arXiv
Addas-Zanata, Salvador Area-preserving diffeomorphisms of the torus whose rotation sets have non-empty interior. (English) Zbl 1351.37176 Ergodic Theory Dyn. Syst. 35, No. 1, 1-33 (2015). MSC: 37E30 37E45 37E40 PDF BibTeX XML Cite \textit{S. Addas-Zanata}, Ergodic Theory Dyn. Syst. 35, No. 1, 1--33 (2015; Zbl 1351.37176) Full Text: DOI arXiv
Simó, Carles Quadratic area-preserving mappings in \({\mathbb R}^2\). (Aplicacions quadràtiques que preserven l’àrea a \(\mathbb{R}^2\).) (Catalan. English summary) Zbl 1371.37088 Butll. Soc. Catalana Mat. 29, No. 1, 77-108 (2014). MSC: 37E30 37E40 37A05 PDF BibTeX XML Cite \textit{C. Simó}, Butll. Soc. Catalana Mat. 29, No. 1, 77--108 (2014; Zbl 1371.37088)
Ostrovski, Georg Dynamics of a continuous piecewise affine map of the square. (English) Zbl 1284.37035 Physica D 271, 1-9 (2014). MSC: 37E30 37D45 37M05 PDF BibTeX XML Cite \textit{G. Ostrovski}, Physica D 271, 1--9 (2014; Zbl 1284.37035) Full Text: DOI arXiv
Martins, C. G. L.; de Carvalho, R. Egydio; Caldas, I. L.; Roberto, M. Labyrinthic standard non-twist map. (English) Zbl 1208.82060 J. Phys. A, Math. Theor. 44, No. 4, Article ID 045102, 9 p. (2011). MSC: 82D10 37D45 37E40 37E45 PDF BibTeX XML Cite \textit{C. G. L. Martins} et al., J. Phys. A, Math. Theor. 44, No. 4, Article ID 045102, 9 p. (2011; Zbl 1208.82060) Full Text: DOI
Guo, Yanhui The approximate properties of Aubry-Mather sets. (Chinese. English summary) Zbl 1150.37369 J. Univ. Sci. Technol. Suzhou, Nat. Sci. 24, No. 2, 16-19 (2007). MSC: 37E40 28D05 37A05 PDF BibTeX XML Cite \textit{Y. Guo}, J. Univ. Sci. Technol. Suzhou, Nat. Sci. 24, No. 2, 16--19 (2007; Zbl 1150.37369)
Le Calvez, Patrice Drift orbits for families of twist maps of the annulus. (English) Zbl 1133.37014 Ergodic Theory Dyn. Syst. 27, No. 3, 869-879 (2007). MSC: 37E40 37J10 37C75 37A05 28D05 PDF BibTeX XML Cite \textit{P. Le Calvez}, Ergodic Theory Dyn. Syst. 27, No. 3, 869--879 (2007; Zbl 1133.37014) Full Text: DOI
Apte, A.; de la Llave, Rafael; Petrov, Nikola P. Regularity of critical invariant circles of the standard nontwist map. (English) Zbl 1074.37026 Nonlinearity 18, No. 3, 1173-1187 (2005). Reviewer: Mike Hurley (Cleveland) MSC: 37E45 37E40 37J10 37J25 PDF BibTeX XML Cite \textit{A. Apte} et al., Nonlinearity 18, No. 3, 1173--1187 (2005; Zbl 1074.37026) Full Text: DOI Link
Oliveira, Fernando Extending circle mappings to the annulus. (English) Zbl 1020.37020 J. Dyn. Differ. Equations 14, No. 4, 829-833 (2002). Reviewer: Mike Hurley (Cleveland) MSC: 37E10 37E30 37E40 PDF BibTeX XML Cite \textit{F. Oliveira}, J. Dyn. Differ. Equations 14, No. 4, 829--833 (2002; Zbl 1020.37020) Full Text: DOI
Murakami, Wakako; Murakami, Chieko; Nomura, Yasuyuki Bifurcation of the period-4 orbits in the standard map. (English) Zbl 0994.37023 Chaos Solitons Fractals 12, No. 10, 1851-1859 (2001). MSC: 37G15 37E40 37J20 PDF BibTeX XML Cite \textit{W. Murakami} et al., Chaos Solitons Fractals 12, No. 10, 1851--1859 (2001; Zbl 0994.37023) Full Text: DOI
VanderVorst, R. C. A. M.; van den Berg, J. B. Periodic orbits for fourth order conservative systems and Morse type theory. (English) Zbl 0966.37032 Fiedler, B. (ed.) et al., International conference on differential equations. Proceedings of the conference, Equadiff ’99, Berlin, Germany, August 1-7, 1999. Vol. 1. Singapore: World Scientific. 241-245 (2000). MSC: 37J45 37E40 PDF BibTeX XML Cite \textit{R. C. A. M. VanderVorst} and \textit{J. B. van den Berg}, in: International conference on differential equations. Proceedings of the conference, Equadiff '99, Berlin, Germany, August 1--7, 1999. Vol. 1. Singapore: World Scientific. 241--245 (2000; Zbl 0966.37032)
Le Calvez, Patrice [Gambaudo, Jean-Marc] Decompositions of diffeomorphisms of the torus in twisted maps (with an appendix in collaboration with Jean-Marc Gambaudo). (Décomposition des difféomorphismes du tore en application déviant la verticale (avec un appendice en collaboration avec Jean-Marc Gambaudo).) (French) Zbl 1039.37023 Mém. Soc. Math. Fr., Nouv. Sér. 79, 148 p. (1999). Reviewer: Olaf Ninnemann (Berlin) MSC: 37E30 37-02 37C25 37E40 37E45 37J45 37J50 PDF BibTeX XML Cite \textit{P. Le Calvez}, Mém. Soc. Math. Fr., Nouv. Sér. 79, 148 p. (1999; Zbl 1039.37023) Full Text: DOI Numdam EuDML
Slijepčević, S. Accelerating orbits of twist diffeomorphisms on a torus. (English) Zbl 0988.37054 Glas. Mat., III. Ser. 34, No. 1, 49-63 (1999). Reviewer: Messoud Efendiev (Berlin) MSC: 37E40 37C40 37E45 37J50 PDF BibTeX XML Cite \textit{S. Slijepčević}, Glas. Mat., III. Ser. 34, No. 1, 49--63 (1999; Zbl 0988.37054)
Simó, C. Invariant curves of analytic perturbed nontwist area preserving maps. (English) Zbl 0932.37048 Regul. Chaotic Dyn. 3, No. 3, 180-195 (1998). MSC: 37J40 37E40 37J35 PDF BibTeX XML Cite \textit{C. Simó}, Regul. Chaotic Dyn. 3, No. 3, 180--195 (1998; Zbl 0932.37048)
Burić, N.; Mudrinić, M.; Todorović, K. Universal scaling of critical quasiperiodic orbits in a class of twist maps. (English) Zbl 0943.37025 J. Phys. A, Math. Gen. 31, No. 39, 7847-7854 (1998). MSC: 37E40 37E45 37C55 PDF BibTeX XML Cite \textit{N. Burić} et al., J. Phys. A, Math. Gen. 31, No. 39, 7847--7854 (1998; Zbl 0943.37025) Full Text: DOI
Gutkin, Eugene; Katok, Anatole Caustics for inner and outer billiards. (English) Zbl 0839.58036 Commun. Math. Phys. 173, No. 1, 101-133 (1995). Reviewer: A.Papadopoulos (Strasbourg) MSC: 37A99 PDF BibTeX XML Cite \textit{E. Gutkin} and \textit{A. Katok}, Commun. Math. Phys. 173, No. 1, 101--133 (1995; Zbl 0839.58036) Full Text: DOI
Ketoja, J. A.; MacKay, R. S. Rotationally-ordered periodic orbits for multiharmonic area-preserving twist maps. (English) Zbl 0814.58012 Physica D 73, No. 4, 388-398 (1994). MSC: 58E07 37G99 PDF BibTeX XML Cite \textit{J. A. Ketoja} and \textit{R. S. MacKay}, Physica D 73, No. 4, 388--398 (1994; Zbl 0814.58012) Full Text: DOI
Mora, Leonardo Birkhoff-Hénon attractors for dissipative perturbations of area- preserving twist maps. (English) Zbl 0817.58023 Ergodic Theory Dyn. Syst. 14, No. 4, 807-815 (1994). Reviewer: B.V.Loginov (Ulyanovsk) MSC: 37C70 PDF BibTeX XML Cite \textit{L. Mora}, Ergodic Theory Dyn. Syst. 14, No. 4, 807--815 (1994; Zbl 0817.58023) Full Text: DOI
Baesens, C.; MacKay, R. S. Cantori for multiharmonic maps. (English) Zbl 0791.58068 Physica D 69, No. 1-2, 59-76 (1993). MSC: 37G99 58E50 74S30 74P10 37J99 PDF BibTeX XML Cite \textit{C. Baesens} and \textit{R. S. MacKay}, Physica D 69, No. 1--2, 59--76 (1993; Zbl 0791.58068) Full Text: DOI
Stirnemann, Andreas Renormalization for golden circles. (English) Zbl 0773.58023 Commun. Math. Phys. 152, No. 2, 369-431 (1993). Reviewer: C.S.Sharma (London) MSC: 37C80 54H25 81T15 PDF BibTeX XML Cite \textit{A. Stirnemann}, Commun. Math. Phys. 152, No. 2, 369--431 (1993; Zbl 0773.58023) Full Text: DOI
Chierchia, L. On a result by J. N. Mather concerning invariant sets for area-preserving twist maps. (English) Zbl 0731.58059 Z. Angew. Math. Phys. 42, No. 1, 80-89 (1991). Reviewer: R.Cowen (Gaborone) MSC: 37C80 37B99 PDF BibTeX XML Cite \textit{L. Chierchia}, Z. Angew. Math. Phys. 42, No. 1, 80--89 (1991; Zbl 0731.58059) Full Text: DOI
Meiss, J. D.; Dewar, R. L. Minimizing flux. (English) Zbl 0728.70020 Chaos and order, Proc. Miniconf., Canberra/Australia 1990, 97-103 (1991). MSC: 70H99 37-XX PDF BibTeX XML
Greene, John M.; Mao, Jian-min Higher-order fixed points of the renormalisation operator for invariant circles. (English) Zbl 0735.70018 Nonlinearity 3, No. 1, 69-78 (1990). Reviewer: W.Sarlet (Gent) MSC: 70K50 37C55 PDF BibTeX XML Cite \textit{J. M. Greene} and \textit{J.-m. Mao}, Nonlinearity 3, No. 1, 69--78 (1990; Zbl 0735.70018) Full Text: DOI
Veerman, J. J. P.; Tangerman, F. M. Renormalization of Aubry-Mather Cantor sets. (English) Zbl 0712.58051 J. Stat. Phys. 56, No. 1-2, 83-98 (1989). MSC: 37J40 37D99 37C80 81T15 PDF BibTeX XML Cite \textit{J. J. P. Veerman} and \textit{F. M. Tangerman}, J. Stat. Phys. 56, No. 1--2, 83--98 (1989; Zbl 0712.58051) Full Text: DOI
Hall, Glen R. Some problems on dynamics of annulus maps. (English) Zbl 0677.58026 Hamiltonian dynamical systems, Proc. AMS-IMS-SIAM Jt. Summer Res. Conf., Boulder/Color. 1987, Contemp. Math. 81, 135-152 (1988). Reviewer: J.Ombach MSC: 37E30 37E45 37J40 PDF BibTeX XML
Denzler, Jochen Mather sets for plane Hamiltonian systems. (English) Zbl 0641.70014 Z. Angew. Math. Phys. 38, 791-812 (1987). Reviewer: M.Z.Nashed MSC: 70H05 37J99 37J40 PDF BibTeX XML Cite \textit{J. Denzler}, Z. Angew. Math. Phys. 38, 791--812 (1987; Zbl 0641.70014) Full Text: DOI
Hall, Glen R. Some examples of permutations modelling area preserving monotone twist maps. (English) Zbl 0637.58042 Physica D 28, 393-400 (1987). MSC: 58Z05 37A99 PDF BibTeX XML Cite \textit{G. R. Hall}, Physica D 28, 393--400 (1987; Zbl 0637.58042) Full Text: DOI
Olvera, Arturo; Simó, Carles The obstruction method and some numerical experiments related to the standard map. (English) Zbl 0628.58046 Periodic solutions of Hamiltonian systems and related topics, Proc. NATO Adv. Res. Workshop, Il Ciocco/Italy 1986, NATO ASI Ser., Ser. C 209, 235-244 (1987). MSC: 37G99 37C80 37J40 PDF BibTeX XML
Chen, Q.; Meiss, J. D.; Percival, I. C. Orbit extension method for finding unstable orbits. (English) Zbl 0625.58029 Physica D 29, No. 1-2, 143-154 (1987). MSC: 37G99 PDF BibTeX XML Cite \textit{Q. Chen} et al., Physica D 29, No. 1--2, 143--154 (1987; Zbl 0625.58029) Full Text: DOI
Veerman, Peter Symbolic dynamics of order-preserving orbits. (English) Zbl 0625.28012 Physica D 29, No. 1-2, 191-201 (1987). MSC: 28D99 PDF BibTeX XML Cite \textit{P. Veerman}, Physica D 29, No. 1--2, 191--201 (1987; Zbl 0625.28012) Full Text: DOI
MacKay, R. S. Hyperbolic cantori have dimension zero. (English) Zbl 0623.58031 J. Phys. A 20, L559-L561 (1987). MSC: 58Z05 37D99 PDF BibTeX XML Cite \textit{R. S. MacKay}, J. Phys. A, Math. Gen. 20, L559--L561 (1987; Zbl 0623.58031) Full Text: DOI
Mather, John N. More Denjoy minimal sets for area preserving diffeomorphisms. (English) Zbl 0597.58015 Comment. Math. Helv. 60, 508-557 (1985). Reviewer: Yu.Kifer MSC: 37A99 PDF BibTeX XML Cite \textit{J. N. Mather}, Comment. Math. Helv. 60, 508--557 (1985; Zbl 0597.58015) Full Text: DOI EuDML
Chenciner, Alain Hamiltonian-like phenomena in saddle-node bifurcations of invariant curves for plane diffeomorphisms. (English) Zbl 0561.58036 Singularities and dynamical systems, Proc. Int. Conf., Heraklion/Greece 1983, North-Holland Math. Stud. 103, 7-14 (1985). Reviewer: R.Devaney MSC: 37G99 PDF BibTeX XML
Aubry, Serge The twist map, the extended Frenkel-Kontorova model and the devil’s staircase. (English) Zbl 0559.58013 Order in chaos, Proc. int. Conf., Los Alamos/N.M. 1982, Physica 7D, 240-258 (1983). Reviewer: F.Przytycki MSC: 37J99 82B26 82B20 PDF BibTeX XML
Winkelnkemper, H. E. Twist maps, coverings and Brouwer’s translation theorem. (English) Zbl 0474.58015 Trans. Am. Math. Soc. 267, 585-593 (1981). MSC: 37C25 37A99 57N05 PDF BibTeX XML Cite \textit{H. E. Winkelnkemper}, Trans. Am. Math. Soc. 267, 585--593 (1981; Zbl 0474.58015) Full Text: DOI
Easton, Robert W. Perturbed twist maps, homoclinic points and ergodic zones. (English) Zbl 0443.58018 Instabilities in dynamical systems, Proc. NATO Adv. Study Inst., Cortina d’Ampezzo 1978, 41-47 (1979). MSC: 37G99 37D99 34D10 PDF BibTeX XML