Zhang, Xiaoming; Li, Denghui; Liu, Xianbin Time-dependent billiards, variational method, and invariant tori. (English) Zbl 07972415 Nonlinearity 38, No. 2, Article ID 025003, 24 p., 24 p. (2025). MSC: 37J40 70F99 70H30 × Cite Format Result Cite Review PDF Full Text: DOI
Dong, Xiujuan; Li, Yong Homoclinic/heteroclinic recurrent orbits and horseshoe. (English) Zbl 07971497 J. Differ. Equations 420, 150-179 (2025). MSC: 34C27 34D10 37B10 37C29 × Cite Format Result Cite Review PDF Full Text: DOI
Crane, Daniel L.; Davidchack, Ruslan L.; Gorban, Alexander N. Minimal cover of high-dimensional chaotic attractors by embedded recurrent patterns. (English) Zbl 07954665 Commun. Nonlinear Sci. Numer. Simul. 140, Part 1, Article ID 108345, 12 p. (2025). MSC: 37M22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Baracco, Luca; Bernardi, Olga Totally integrable symplectic billiards are ellipses. (English) Zbl 07900776 Adv. Math. 454, Article ID 109873, 17 p. (2024). Reviewer: Daniel Jaud (München) MSC: 37E40 37J39 37J35 37C83 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Baracco, Luca; Bernardi, Olga; Nardi, Alessandra Higher order terms of Mather’s \(\beta\)-function for symplectic and outer billiards. (English) Zbl 1544.37041 J. Math. Anal. Appl. 537, No. 2, Article ID 128353, 20 p. (2024). MSC: 37E40 37C83 53A15 52A27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bessa, Mário; Del Magno, Gianluigi; Lopes Dias, João; Gaivão, José Pedro; Torres, Maria Joana Billiards in generic convex bodies have positive topological entropy. (English) Zbl 1541.37033 Adv. Math. 442, Article ID 109592, 39 p. (2024). MSC: 37D05 37C83 37B40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bolotin, S.; Treschev, D. Another billiard problem. (English) Zbl 1540.37084 Russ. J. Math. Phys. 31, No. 1, 50-59 (2024). MSC: 37J39 37C83 37D40 × Cite Format Result Cite Review PDF Full Text: DOI
Qu, Huadi; Xia, Zhihong Action and periodic orbits of area-preserving diffeomorphisms. (English) Zbl 1543.37050 J. Differ. Equations 391, 246-264 (2024). MSC: 37E30 37E35 37A05 37C05 37J46 37J51 × Cite Format Result Cite Review PDF Full Text: DOI
Ghanbari, Behzad; Kumar, Sunil A study on fractional predator-prey-pathogen model with Mittag-Leffler kernel-based operators. (English) Zbl 1531.92010 Numer. Methods Partial Differ. Equations 40, No. 1, Article ID e22689, 17 p. (2024). MSC: 92-08 34A08 65P20 92D25 × Cite Format Result Cite Review PDF Full Text: DOI
Castro, Fábio; Oliveira, Fernando Most invariant manifolds of conservative systems have transitive closure. (English) Zbl 1535.37033 Differ. Equ. Dyn. Syst. 32, No. 1, 1-13 (2024). MSC: 37C79 37C20 37C10 × Cite Format Result Cite Review PDF Full Text: DOI
Agapov, Sergei; Shubin, Vladislav New examples of non-polynomial integrals of two-dimensional geodesic flows. (English) Zbl 1530.53083 J. Phys. A, Math. Theor. 57, No. 1, Article ID 015204, 17 p. (2024). Reviewer: Alexey O. Remizov (Moskva) MSC: 53D25 53C22 37J35 37J39 37D40 × Cite Format Result Cite Review PDF Full Text: DOI
Chartier, Jean; de Mesmay, Arnaud Finding weakly simple closed quasigeodesics on polyhedral spheres. (English) Zbl 1540.52023 Discrete Comput. Geom. 71, No. 1, 95-120 (2024). Reviewer: Samyon R. Nasyrov (Kazan) MSC: 52B70 53C22 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Takeuchi, Airi; Zhao, Lei Conformal transformations and integrable mechanical billiards. (English) Zbl 1535.37036 Adv. Math. 436, Article ID 109411, 31 p. (2024). Reviewer: Thomas B. Ward (Durham) MSC: 37C83 37J35 70F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Takeuchi, Airi; Zhao, Lei Projective integrable mechanical billiards. (English) Zbl 1533.37074 Nonlinearity 37, No. 1, Article ID 015011, 27 p. (2024). MSC: 37C83 37J35 70F35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Anderson, Keegan D. Dynamics of a rotated orthogonal gravitational wedge billiard. (English) Zbl 1546.37044 Int. J. Bifurcation Chaos Appl. Sci. Eng. 33, No. 12, Article ID 2350136, 8 p. (2023). MSC: 37C83 37J35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Schwartz, Richard Evan Survey lecture on billiards. (English) Zbl 1543.37001 Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 4. Sections 5–8. Berlin: European Mathematical Society (EMS). 2392-2429 (2023). Reviewer: Thomas B. Ward (Durham) MSC: 37-02 37C83 37C55 37C35 37D40 37J70 32G15 × Cite Format Result Cite Review PDF Full Text: DOI
Barrow-Green, June George Birkhoff’s forgotten manuscript and his programme for dynamics. (English) Zbl 1537.01035 Beliaev, Dmitry (ed.) et al., International congress of mathematicians 2022, ICM 2022, Helsinki, Finland, virtual, July 6–14, 2022. Volume 7. Sections 15–20. Berlin: European Mathematical Society (EMS). 5748-5770 (2023). MSC: 01A60 37-03 37B99 × Cite Format Result Cite Review PDF Full Text: DOI
Boeva, Anna Vyacheslavovna; Mukhin, Ravil’ Rafkatovich Calculus of variations in the large: birth, formation, applications. (Russian. English summary) Zbl 1539.49001 Chebyshevskiĭ Sb. 24, No. 3(89), 263-288 (2023). MSC: 49-03 58E05 01A55 01A60 01A61 49K10 49J10 × Cite Format Result Cite Review PDF Full Text: DOI MNR
Corvaja, Pietro; Zannier, Umberto [Demeio, Julian Lawrence] Finiteness theorems on elliptical billiards and a variant of the dynamical Mordell-Lang conjecture. (English) Zbl 1541.14043 Proc. Lond. Math. Soc. (3) 127, No. 5, 1268-1337 (2023). Reviewer: Jan-Hendrik Evertse (Leiden) MSC: 14G99 37C25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Qiu, Zhiping; Qiu, Yu Symplectic central difference scheme for quasi-linear autonomous Birkhoffian systems. (English) Zbl 1511.65143 Appl. Math. Comput. 440, Article ID 127661, 15 p. (2023). MSC: 65P10 37M15 65L06 70H05 × Cite Format Result Cite Review PDF Full Text: DOI
Flosi, J.; Lamarque, C.-H.; Savadkoohi, A. Ture Periodic solutions of approximated normal forms and simplification of normal transform by using Gröbner basis. (English) Zbl 1505.34059 Appl. Math. Modelling 109, 808-818 (2022). MSC: 34C20 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Koudjinan, Comlan E.; Kaloshin, Vadim On some invariants of Birkhoff billiards under conjugacy. (English) Zbl 1507.37035 Regul. Chaotic Dyn. 27, No. 5, 525-537 (2022). MSC: 37C83 37J35 37J39 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Artigue, Alfonso On continuum-wise minimality. (English) Zbl 1507.37011 Fundam. Math. 258, No. 3, 265-289 (2022). MSC: 37B05 37B45 × Cite Format Result Cite Review PDF Full Text: DOI
Berger, Pierre; Crovisier, Sylvain; Pujals, Enrique Germ-typicality of the coexistence of infinitely many sinks. (English) Zbl 1503.37038 Adv. Math. 407, Article ID 108528, 51 p. (2022). MSC: 37C20 37C29 37C75 37G20 37G25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Vales, Túlio; Pinto-de-Carvalho, Sônia A random billiard map in the circle. (English) Zbl 1498.37048 Dyn. Syst. 37, No. 2, 333-353 (2022). MSC: 37C83 37H10 37H12 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Huang, Guan On the integrability of strictly convex billiard tables with boundaries close to ellipses with small eccentricities. (English) Zbl 1490.37078 Acta Math. Sin., Engl. Ser. 38, No. 1, 55-67 (2022). MSC: 37J35 37J39 37C83 37E40 × Cite Format Result Cite Review PDF Full Text: DOI
Hireche, Faouzi; Ghomari, Kaoutar Spectrum of semiclassical Schrödinger operators for two-frequency resonance. (English) Zbl 1509.35257 Asymptotic Anal. 127, No. 1-2, 191-200 (2022). MSC: 35Q40 81Q05 81S10 37G05 35B34 × Cite Format Result Cite Review PDF Full Text: DOI
Deng, Yanxia; Offin, Daniel Stability of periodic orbits by Conley-Zehnder index theory. (English) Zbl 1494.37037 J. Differ. Equations 314, 473-490 (2022). Reviewer: Zdzisław Dzedzej (Gdańsk) MSC: 37J25 37J51 37B30 34D20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kaloshin, Vadim; Sorrentino, Alfonso Inverse problems and rigidity questions in billiard dynamics. (English) Zbl 1495.37029 Ergodic Theory Dyn. Syst. 42, No. 3, 1023-1056 (2022). MSC: 37C83 37E40 37J35 37J46 37J51 37J70 58J50 × Cite Format Result Cite Review PDF Full Text: DOI
Gérard, Patrick; Kappeler, Thomas; Topalov, Petar On the analytic Birkhoff normal form of the Benjamin-Ono equation and applications. (English) Zbl 1521.37085 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 216, Article ID 112687, 32 p. (2022). MSC: 37K55 35Q51 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tzemos, A. C.; Contopoulos, G. Order and chaos in time periodic Hamiltonian systems. (English) Zbl 1491.37058 Physica D 419, Article ID 132847, 12 p. (2021). MSC: 37J46 37J12 34C28 65P10 × Cite Format Result Cite Review PDF Full Text: DOI
Bastos, Jefferson L. R.; Buzzi, Claudio A.; Torregrosa, Joan Orbitally symmetric systems with applications to planar centers. (English) Zbl 1493.34120 Commun. Pure Appl. Anal. 20, No. 10, 3319-3347 (2021). Reviewer: Maite Grau (Lleida) MSC: 34C14 34C25 34C07 34C05 × Cite Format Result Cite Review PDF Full Text: DOI
Hanusa, Christopher R. H.; Mahankali, Arvind V. A billiards-like dynamical system for attacking chess pieces. (English) Zbl 1471.37034 Eur. J. Comb. 95, Article ID 103341, 26 p. (2021). MSC: 37C83 37C55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lerman, L. M.; Trifonov, K. N. Saddle-center and periodic orbit: dynamics near symmetric heteroclinic connection. (English) Zbl 1465.37074 Chaos 31, No. 2, Article ID 023113, 17 p. (2021). MSC: 37J46 37C29 37C27 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Anderson, Keegan D.; Villet, Charles M. Computational study of the dynamics of an asymmetric wedge billiard. (English) Zbl 1462.37088 Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 2, Article ID 2130006, 11 p. (2021). MSC: 37M05 37C83 70F35 65P20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gasiorek, Sean; Radnović, Milena Pseudo-Euclidean billiards within confocal curves on the hyperboloid of one sheet. (English) Zbl 1464.14036 J. Geom. Phys. 161, Article ID 104032, 22 p. (2021). Reviewer: Ahmed Lesfari (El Jadida) MSC: 14H70 37J35 70H06 70H12 37J38 37J39 37J46 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Xu, Xin-Xin; Zhang, Yi A new type of adiabatic invariants for disturbed Birkhoffian system of Herglotz type. (English) Zbl 07830269 Chin. J. Phys., Taipei 64, 278-286 (2020). MSC: 70H30 37J46 70G75 × Cite Format Result Cite Review PDF Full Text: DOI
Efremova, L. S. Small \(C^1\)-smooth perturbations of skew products and the partial integrability property. (English) Zbl 1524.37033 Appl. Math. Nonlinear Sci. 5, No. 2, 317-328 (2020). MSC: 37E05 37J70 37C75 × Cite Format Result Cite Review PDF Full Text: DOI
Page, Gregory; Antoine, Charles; Dettmann, Carl P.; Talbot, Julian The Iris billiard: critical geometries for global chaos. (English) Zbl 1457.37043 Chaos 30, No. 12, 123105, 22 p. (2020). MSC: 37C83 37M05 70K55 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Lin-Jie; Zhang, Yi Non-standard Birkhoffian dynamics and its Noether’s theorems. (English) Zbl 1477.70032 Commun. Nonlinear Sci. Numer. Simul. 91, Article ID 105435, 16 p. (2020). MSC: 70H30 70G75 70H33 37J51 × Cite Format Result Cite Review PDF Full Text: DOI
Kourliouros, Konstantinos Relative logarithmic cohomology and Nambu structures of maximal degree. (English. French summary) Zbl 1453.32030 J. Math. Pures Appl. (9) 144, 250-268 (2020). MSC: 32S05 32S30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Blagojević, Pavle V. M.; Harrison, Michael; Tabachnikov, Serge; Ziegler, Günter M. Counting periodic trajectories of Finsler billiards. (English) Zbl 1451.37035 SIGMA, Symmetry Integrability Geom. Methods Appl. 16, Paper 022, 33 p. (2020). Reviewer: Thomas J. Bartsch (Gießen) MSC: 37C83 37J46 37C55 55R80 58E05 70H12 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Reznik, Dan; Garcia, Ronaldo; Koiller, Jair Can the elliptic billiard still surprise us? (English) Zbl 1439.37031 Math. Intell. 42, No. 1, 6-17 (2020). MSC: 37C83 37J40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ehrnström, Mats; Wang, Yuexun Enhanced existence time of solutions to the fractional Korteweg-de Vries equation. (English) Zbl 1419.76063 SIAM J. Math. Anal. 51, No. 4, 3298-3323 (2019). MSC: 76B03 35S30 76B15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sun, Guanghui; Fu, Xilin Discontinuous dynamics of a class of oscillators with strongly nonlinear asymmetric damping under a periodic excitation. (English) Zbl 1473.70049 Commun. Nonlinear Sci. Numer. Simul. 61, 230-247 (2018). MSC: 70K42 34A36 34C25 × Cite Format Result Cite Review PDF Full Text: DOI
Kaloshin, Vadim; Sorrentino, Alfonso On the integrability of Birkhoff billiards. (English) Zbl 1407.37085 Philos. Trans. R. Soc. Lond., A, Math. Phys. Eng. Sci. 376, No. 2131, Article ID 20170419, 16 p. (2018). MSC: 37J05 37D50 × Cite Format Result Cite Review PDF Full Text: DOI
López, Álvaro G.; Daza, Álvar; Seoane, Jesús M.; Sanjuán, Miguel A. F. Computing complex horseshoes by means of piecewise maps. (English) Zbl 1403.37043 Int. J. Bifurcation Chaos Appl. Sci. Eng. 28, No. 12, Article ID 1830039, 11 p. (2018). MSC: 37D45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kaloshin, Vadim; Sorrentino, Alfonso On the local Birkhoff conjecture for convex billiards. (English) Zbl 1394.37093 Ann. Math. (2) 188, No. 1, 315-380 (2018). Reviewer: William J. Satzer Jr. (St. Paul) MSC: 37J35 70H06 37E40 33E05 37D50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Huang, Guan; Kaloshin, Vadim; Sorrentino, Alfonso Nearly circular domains which are integrable close to the boundary are ellipses. (English) Zbl 1395.37041 Geom. Funct. Anal. 28, No. 2, 334-392 (2018). Reviewer: William J. Satzer Jr. (St. Paul) MSC: 37J35 37D50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Dettmann, Carl P.; Fain, Vitaly; Turaev, Dmitry Splitting of separatrices, scattering maps, and energy growth for a billiard inside a time-dependent symmetric domain close to an ellipse. (English) Zbl 1388.37067 Nonlinearity 31, No. 3, 667-700 (2018). Reviewer: Vladimir Răsvan (Craiova) MSC: 37J40 37C29 37C50 37J25 70H09 70K55 70K70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Huang, Guan; Kaloshin, Vadim; Sorrentino, Alfonso On the marked length spectrum of generic strictly convex billiard tables. (English) Zbl 1417.37138 Duke Math. J. 167, No. 1, 175-209 (2018). MSC: 37D50 37E40 37J50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Grines, V. Z.; Zhuzhoma, Ye. V.; Pochinka, Olga V. Rough diffeomorphisms with basic sets of codimension one. (English. Russian original) Zbl 1379.37049 J. Math. Sci., New York 225, No. 2, 195-219 (2017); translation from Sovrem. Mat., Fundam. Napravl. 57, 5-30 (2015). MSC: 37C15 37C05 37C75 37D20 × Cite Format Result Cite Review PDF Full Text: DOI
Zhai, Xiang-Hua; Zhang, Yi Noether symmetries and conserved quantities for fractional Birkhoffian systems with time delay. (English) Zbl 1470.34104 Commun. Nonlinear Sci. Numer. Simul. 36, 81-97 (2016). MSC: 34C14 34K05 34K37 × Cite Format Result Cite Review PDF Full Text: DOI
Markeev, A. P. The stability of two-link trajectories of a Birkhoff billiard. (English. Russian original) Zbl 1434.70043 J. Appl. Math. Mech. 80, No. 4, 280-289 (2016); translation from Prikl. Mat. Mekh. 80, No. 4, 403-416 (2016). MSC: 70H14 37C83 37J25 × Cite Format Result Cite Review PDF Full Text: DOI
Huaraca, Walter; Mendoza, Valentín Minimal topological chaos coexisting with a finite set of homoclinic and periodic orbits. (English) Zbl 1364.37072 Physica D 315, 83-89 (2016). MSC: 37D20 37E30 × Cite Format Result Cite Review PDF Full Text: DOI Link
Markeev, A. P. On the stability of periodic trajectories of a planar Birkhoff billiard. (English. Russian original) Zbl 1383.37029 Proc. Steklov Inst. Math. 295, 190-201 (2016); translation from Tr. Mat. Inst. Steklova 295, 206-217 (2016). MSC: 37D50 37J25 70H12 70H14 × Cite Format Result Cite Review PDF Full Text: DOI
Yan, Dongfeng Constructing invariant tori for the spatial Hill lunar problem. (English) Zbl 1334.37056 Chin. Ann. Math., Ser. B 37, No. 1, 125-136 (2016). MSC: 37J15 37J40 37J25 70M20 × Cite Format Result Cite Review PDF Full Text: DOI
Wang, Tao; Yin, Jian Dong; Yan, Qi Several transitive properties and Devaney’s chaos. (English) Zbl 1344.54006 Acta Math. Sin., Engl. Ser. 32, No. 3, 373-383 (2016). Reviewer: Mihai Turinici (Iaşi) MSC: 54H20 37D45 37B45 × Cite Format Result Cite Review PDF Full Text: DOI
Sorrentino, Alfonso Computing Mather’s \(\beta\)-function for Birkhoff billiards. (English) Zbl 1359.37088 Discrete Contin. Dyn. Syst. 35, No. 10, 5055-5082 (2015). MSC: 37D50 37E40 37J50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Alkoumi, Naeem; Schlenk, Felix Shortest closed billiard orbits on convex tables. (English) Zbl 1359.37086 Manuscr. Math. 147, No. 3-4, 365-380 (2015). MSC: 37D50 37J05 52A10 52A40 53D05 52A20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Pecker, Daniel Poncelet’s theorem and billiard knots. (English) Zbl 1282.57011 Geom. Dedicata 161, 323-333 (2012). MSC: 57M25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL Backlinks: MO
Fetter, Hans L. Numerical exploration of a hexagonal string billiard. (English) Zbl 1300.37027 Physica D 241, No. 8, 830-846 (2012). MSC: 37D50 70F35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mikoss, I.; García, P. An exact map for a chaotic billiard. (English) Zbl 1218.37119 Int. J. Mod. Phys. B 25, No. 5, 673-681 (2011). MSC: 37N20 37D50 81Q50 × Cite Format Result Cite Review PDF Full Text: DOI
Benet, Luis; Merlo, Olivier Phase-space volume of regions of trapped motion: Multiple ring components and arcs. (English) Zbl 1157.70016 Celest. Mech. Dyn. Astron. 103, No. 3, 209-225 (2009). MSC: 70K05 70K30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Markeev, A. P. Dynamics of a rigid body that collides with a rigid surface. (Russian. English summary) Zbl 07956424 Nelineĭn. Din. 4, No. 1, 1-38 (2008). MSC: 70E15 70F35 70E50 70H05 × Cite Format Result Cite Review PDF Full Text: MNR
Markeev, A. P. The dynamics of a rigid body colliding with a rigid surface. (English) Zbl 1229.70010 Regul. Chaotic Dyn. 13, No. 2, 96-129 (2008). MSC: 70E15 70F35 70E50 70H05 × Cite Format Result Cite Review PDF Full Text: DOI
Kruglikov, Boris Invariant characterization of Liouville metrics and polynomial integrals. (English) Zbl 1145.53067 J. Geom. Phys. 58, No. 8, 979-995 (2008). MSC: 53D25 53B20 37J15 53A55 70H06 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gutiérrez, E.; Arrowsmith, D. K. The equivalence between feedback and dissipation in impact oscillators. (English) Zbl 1136.70325 Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 1, 255-269 (2007). MSC: 70K55 70Q05 93D15 70K30 × Cite Format Result Cite Review PDF Full Text: DOI
Steiner, F. Quantum chaos. (Russian. English summary) Zbl 07956282 Nelineĭn. Din. 2, No. 2, 214-235 (2006). MSC: 37-XX × Cite Format Result Cite Review PDF Full Text: MNR
Bernardi, Olga; Cardin, Franco Poincaré-Birkhoff periodic orbits for mechanical Hamiltonian systems on \(t^{*} \mathbb T^{n}\). (English) Zbl 1112.37039 J. Math. Phys. 47, No. 7, 072701, 15 p. (2006). MSC: 37Jxx 58Exx 70Hxx × Cite Format Result Cite Review PDF Full Text: DOI
Baryshnikov, Y.; Zharnitsky, V. Billiards and nonholonomic distributions. (English. Russian original) Zbl 1120.37033 J. Math. Sci., New York 128, No. 2, 2706-2710 (2005); translation from Zap. Nauchn. Semin. POMI 300, 56-64 (2003). MSC: 37J10 37D50 37J60 70H05 × Cite Format Result Cite Review PDF Full Text: DOI
Armstead, Douglas N.; Hunt, Brian R.; Ott, Edward Power-law decay and self-similar distributions in stadium-type billiards. (English) Zbl 1059.37026 Physica D 193, No. 1-4, 96-127 (2004). MSC: 37D50 37J10 × Cite Format Result Cite Review PDF Full Text: DOI
Cheng, Wei; Cheng, Chongqing Existence of infinite non-Birkhoff periodic orbits for area-preserving monotone twist maps of cylinders. (English) Zbl 0998.37017 Sci. China, Ser. A 43, No. 8, 810-817 (2000). Reviewer: Rafael Ortega (Granada) MSC: 37J45 37E40 34C25 × Cite Format Result Cite Review PDF Full Text: DOI
Lebœuf, P.; Mouchet, A. Normal forms and complex periodic orbits in semiclassical expansions of Hamiltonian systems. (English) Zbl 1039.81024 Ann. Phys. 275, No. 1, 54-112 (1999). MSC: 81Q20 70H05 34C23 37J40 81Q50 70K45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Siegelmann, Hava T.; Fishman, Shmuel Analog computation with dynamical systems. (English) Zbl 0954.37038 Physica D 120, No. 1-2, 214-235 (1998). MSC: 37M99 68Q15 65P99 × Cite Format Result Cite Review PDF Full Text: DOI
Collas, Peter; Klein, David; Schwebler, Hans-Peter Convergence of Hamiltonian systems to billiards. (English) Zbl 0986.37050 Chaos 8, No. 2, 466-474 (1998). MSC: 37J35 37D50 70H14 65P10 × Cite Format Result Cite Review PDF Full Text: DOI Link
Nakamura, Katsuhiro Introduction to chaos and quantum transport. (English) Zbl 0935.81028 Chaos Solitons Fractals 8, No. 7-8, 971-993 (1997). MSC: 81Q50 37D45 37N20 × Cite Format Result Cite Review PDF Full Text: DOI
Mira, Christian Some historical aspects of nonlinear dynamics – possible trends for the future. (English) Zbl 0901.34003 J. Franklin Inst. 334B, No. 5-6, 1075-1113 (1997). MSC: 34-03 70-03 37-XX 01A75 × Cite Format Result Cite Review PDF Full Text: DOI
Ji, Min Multiplicity of periodic solutions to Birkhoff’s billiard ball problem. (English) Zbl 0889.58065 Chin. Sci. Bull. 42, No. 5, 353-355 (1997). Reviewer: E.Ershov (St.Peterburg) MSC: 37G99 28D05 × Cite Format Result Cite Review PDF Full Text: DOI
Tabanov, M. B. Veiled assonance between geodesics on ellipsoid and billiard in its focal ellipse. (English) Zbl 0980.53099 J. Geom. Phys. 19, No. 4, 399-413 (1996). MSC: 53D25 37D50 37K25 70H20 37D40 53C22 × Cite Format Result Cite Review PDF Full Text: DOI
Castilho, César; de Almeida, A. M. Ozorio Semiclassical limit for a truncated Hamiltonian. (English) Zbl 1260.82093 Chaos 6, No. 2, 172-183 (1996). MSC: 82D50 82D20 11F72 × Cite Format Result Cite Review PDF Full Text: DOI
Tabanov, M. B. New ellipsoidal confocal coordinates and geodesics on an ellipsoid. (English) Zbl 0889.58062 J. Math. Sci., New York 82, No. 6, 3851-3858 (1996). Reviewer: U.Hamenstädt (Bonn) MSC: 37D40 53D25 37J35 37K10 × Cite Format Result Cite Review PDF Full Text: DOI
Howard, J. E.; Humpherys, J. Nonmonotonic twist maps. (English) Zbl 0888.58055 Physica D 80, No. 3, 256-276 (1995). MSC: 37C55 37G99 × Cite Format Result Cite Review PDF Full Text: DOI
Sekar, P.; Narayanan, S. Chaos in mechanical systems – a review. (English) Zbl 1014.37023 Sādhanā 20, No. 2-4, 529-582 (1995). MSC: 37D45 37-02 70K50 74Hxx × Cite Format Result Cite Review PDF Full Text: DOI
Bunimovich, Leonid A. Variational principle for periodic trajectories of hyperbolic billiards. (English) Zbl 1055.37549 Chaos 5, No. 2, 349-355 (1995). MSC: 37D50 37D45 70F35 × Cite Format Result Cite Review PDF Full Text: DOI
Tabanov, M. B. Separatrices splitting for Birkhoff’s billiard in symmetric convex domain, closed to an ellipse. (English) Zbl 1055.37551 Chaos 4, No. 4, 595-606 (1994). MSC: 37D50 70H03 × Cite Format Result Cite Review PDF Full Text: DOI
Amiran, Edoh Y. A dynamical approach to symplectic and spectral invariants for billiards. (English) Zbl 0786.58034 Commun. Math. Phys. 154, No. 1, 99-110 (1993). Reviewer: G.Warnecke (Stuttgart) MSC: 37C80 37J99 37B99 53C15 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Jensen, R. V. Chaotic scattering, unstable periodic orbits, and fluctuations in quantum transport. (English) Zbl 0899.58057 Chaos 1, No. 1, 101-109 (1991). MSC: 37N99 82C70 81Q50 × Cite Format Result Cite Review PDF Full Text: DOI
Bunimovich, L. A. Many-dimensional nowhere dispersing billiards with chaotic behavior. (English) Zbl 0679.58030 Physica D 33, No. 1-3, 58-64 (1988). MSC: 37D45 × Cite Format Result Cite Review PDF Full Text: DOI
Da Silva Ritter, G. L.; Ozorio de Almeida, A. M.; Douady, R. Analytical determination of unstable periodic orbits in area preserving maps. (English) Zbl 0628.34043 Physica D 29, No. 1-2, 181-190 (1987). MSC: 34C25 37G99 × Cite Format Result Cite Review PDF Full Text: DOI
Casdagli, Martin Periodic orbits for dissipative twist maps. (English) Zbl 0596.58038 Ergodic Theory Dyn. Syst. 7, 165-173 (1987). MSC: 37G99 58E30 × Cite Format Result Cite Review PDF Full Text: DOI
Mather, John A criterion for the non-existence of invariant circles. (English) Zbl 0603.58028 Publ. Math., Inst. Hautes Étud. Sci. 63, 153-204 (1986). Reviewer: Ding Tongren MSC: 37G99 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Hayli, A.; Dumont, Th. Experiences numeriques sur des billards \(C^ 1\) formes de quatre arcs de cercles. (Numerical exploration of \(C^ 1\)-billiards constructed with four arcs of circles). (French) Zbl 0602.70022 Celestial Mech. 38, 23-66 (1986). Reviewer: G.Jumarie MSC: 70K05 70F15 × Cite Format Result Cite Review PDF Full Text: DOI
Chenciner, A. Bifurcations de points fixes elliptiques. II: Orbites periodiques et ensembles de Cantor invariants. (Bifurcations of elliptic fixed points. II: Periodic orbits and invariant Cantor sets). (French) Zbl 0578.58031 Invent. Math. 80, 81-106 (1985). MSC: 37G99 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
de Glas, Michel Invariance and stability of fuzzy systems. (English) Zbl 0557.93060 J. Math. Anal. Appl. 99, 299-319 (1984). Reviewer: R.Vachnadze MSC: 93D99 37C80 94D05 03E72 93B25 × Cite Format Result Cite Review PDF Full Text: DOI
Hirsch, Morris W. The dynamical systems approach to differential equations. (English) Zbl 0541.34026 Bull. Am. Math. Soc., New Ser. 11, 1-64 (1984). Reviewer: N.H.Pavel MSC: 35B05 37C10 00A30 47H20 47H07 37N99 37C75 37C70 01A45 × Cite Format Result Cite Review PDF Full Text: DOI
Mather, John N. Non-uniqueness of solutions of Percival’s Euler-Lagrange equation. (English) Zbl 0553.58011 Commun. Math. Phys. 86, 465-473 (1982). MSC: 37J99 37G99 70G99 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Rogers, Thomas D.; Clarke, Bruce L. A continuous planar map with many periodoc points. (English) Zbl 0475.39005 Appl. Math. Comput. 8, 17-33 (1981). MSC: 39A10 65Q05 39A12 92D25 × Cite Format Result Cite Review PDF Full Text: DOI
Danby, J. M. A. The evolution of periodic orbits close to homoclinic points. (English) Zbl 0267.70007 Celestial Mech. 8, 273-280 (1973). MSC: 70G10 × Cite Format Result Cite Review PDF Full Text: DOI
Zehnder, E. Homoclinic points near elliptic fixed points. (English) Zbl 0261.58002 Commun. Pure Appl. Math. 26, 131-182 (1973). MSC: 37J99 37C25 × Cite Format Result Cite Review PDF Full Text: DOI