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Jha, Sangita (ed.) et al., Recent developments in fractal geometry and dynamical systems. AMS special session. Fractal geometry and dynamical systems, virtual, May 14–15, 2022. Providence, RI: American Mathematical Society (AMS). Contemp. Math. 797, 75-83 (2024).

MSC: 37A60 37A25 37C75 37C79 37C83

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Frączek, Krzysztof; Ulcigrai, Corinna

On the asymptotic growth of Birkhoff integrals for locally Hamiltonian flows and ergodicity of their extensions. (English) Zbl 1542.37003

Comment. Math. Helv. 99, No. 2, 231-354 (2024).

Reviewer: Jayadev Athreya (Seattle)

MSC: 37A10 37E35 37E05 37A40 37A30 37C83

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Chaika, Jon; Weiss, Barak

On the ergodic theory of the real Rel foliation. (English) Zbl 1543.37034

Forum Math. Pi 12, Paper No. e7, 25 p. (2024).

MSC: 37C86 37D40 37A25 37A35 57M50

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Jin, Xin; Zhang, Pengfei

Homoclinic and heteroclinic intersections for lemon billiards. (English) Zbl 1541.37030

Adv. Math. 442, Article ID 109588, 67 p. (2024).

MSC: 37C83 37C29 37E30 37B40 37A35

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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

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Araújo Lima, T.; do Carmo, R. B.

Classical and quantum elliptical billiards: mixed phase space and short-range correlations in singlets and doublets. (English) Zbl 1541.81201

Physica D 458, Article ID 134018, 8 p. (2024).

MSC: 81U40 81Q50 37C83 81P68 81Q20 35P15

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Delarue, Benjamin; Schütte, Philipp; Weich, Tobias

Resonances and weighted zeta functions for obstacle scattering via smooth models. (English) Zbl 1537.37036

Ann. Henri Poincaré 25, No. 2, 1607-1656 (2024).

MSC: 37C83 37C30 37D40 37D20 37D25 37A46

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Climenhaga, Vaughn; Demers, Mark F.; Lima, Yuri; Zhang, Hongkun

Lyapunov exponents and nonadapted measures for dispersing billiards. (English) Zbl 1537.37035

Commun. Math. Phys. 405, No. 2, Paper No. 24, 13 p. (2024).

Reviewer: Thomas B. Ward (Durham)

MSC: 37C83 37C30 37D25 37A60

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Demers, Mark F.; Korepanov, Alexey

Rates of mixing for the measure of maximal entropy of dispersing billiard maps. (English) Zbl 1536.37006

Proc. Lond. Math. Soc. (3) 128, No. 1, Article ID e12578, 38 p. (2024).

Reviewer: Thomas B. Ward (Durham)

MSC: 37A50 37A25 37C83 60F05

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Kryzhevich, Sergey; Plakhov, Alexander

Rotating rod and ball. (English) Zbl 1536.70016

J. Math. Anal. Appl. 533, No. 1, Article ID 128018, 19 p. (2024).

MSC: 70F35 37C83

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Dragović, Vladimir; Mironov, Andrey E.

On differential equations of integrable billiard tables. (English) Zbl 1535.37034

Acta Math. Sin., Engl. Ser. 40, No. 1, 417-424 (2024).

Reviewer: Daniel Jaud (München)

MSC: 37C83 37J35 37J39 70H06

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Hasselblatt, Boris; Yeun Kim, Ki; Levi, Mark

Cusps in heavy billiards. (English) Zbl 1536.37033

Nonlinearity 37, No. 2, Article ID 025006, 21 p. (2024).

Reviewer: Daniel Jaud (München)

MSC: 37C83 37N05 70F35

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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

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Gonçalves Ferreira, Geraldo César; Oliffson Kamphorst, Sylvie; Pinto-de-Carvalho, Sônia

Symmetric periodic orbits in symmetric billiards. (English) Zbl 1533.37073

Nonlinearity 37, No. 1, Article ID 015005, 16 p. (2024).

MSC: 37C83 37C79 37C20 37C29 37J30 37J35

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Beck, József; Chen, William W. L.; Yang, Yuxuan

Non-integrable dynamics. Time-quantitative results. (English) Zbl 07745800

Singapore: World Scientific (ISBN 978-981-12-7385-8/hbk; 978-981-12-7387-2/ebook). xv, 384 p. (2024).

Reviewer: William J. Satzer Jr. (St. Paul)

MSC: 37-02 37E30 37C35 37E35 37C83 37J30 37D40 70K55

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Anastassiou, Stavros

Planar vector fields in the kernel of a 1–form. arXiv:2411.07587

Preprint, arXiv:2411.07587 [math.DS] (2024).

MSC: 37C15 37G05 58K45

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Sánchez, Percy Fernández; Fernández, Jorge Mozo

Generalized Poincaré-Dulac singularities of holomorphic foliations. arXiv:2411.02873

Preprint, arXiv:2411.02873 [math.DS] (2024).

MSC: 32S65 37C15

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Filimonov, Dmitry A.; Ilyashenko, Yulij S.

Singular points in generic two-parameter families of vector fields on 2-manifold. arXiv:2410.11465

Preprint, arXiv:2410.11465 [math.DS] (2024).

MSC: 37G10 58K45 34C23

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Arana-Herrera, Francisco; Chaika, Jon; Forni, Giovanni

Weak mixing in rational billiards. arXiv:2410.11117

Preprint, arXiv:2410.11117 [math.DS] (2024).

MSC: 37A25 37C83 37E35 37F34

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Kontorovich, Alex; Zhang, Xin

On the Local-Global Conjecture for Combinatorial Period Lengths of Closed Billiards on the Regular Pentagon. arXiv:2409.10682

Preprint, arXiv:2409.10682 [math.NT] (2024).

MSC: 37C83 11E20 11F41

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Dragović, Vladimir; Radnović, Milena

Magic Billiards: the Case of Elliptical Boundaries. arXiv:2409.03158

Preprint, arXiv:2409.03158 [math.DS] (2024).

MSC: 37C83 37J35 37J39

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Bruin, Henk; Lukina, Olga

Skew-product systems over infinite interval exchange transformations. arXiv:2408.14079

Preprint, arXiv:2408.14079 [math.DS] (2024).

MSC: 37C83 37E05 28D05 37B10 37E20 37E35

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Koval, Illya; Vig, Amir

Silent Orbits and Cancellations in the Wave Trace. arXiv:2408.09238

Preprint, arXiv:2408.09238 [math.SP] (2024).

MSC: 35P20 37C83 58C40 58J53

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Marklof, Jens; Pollicott, Mark

Extreme events for horocycle flows. arXiv:2408.01781

Preprint, arXiv:2408.01781 [math.DS] (2024).

MSC: 37D40 37D50 11B57

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Glutsyuk, Alexey; Matveev, Vladimir S.

If a Minkowski billiard is projective, it is the standard billiard. arXiv:2407.20159

Preprint, arXiv:2407.20159 [math.DS] (2024).

MSC: 37C83 37D40 53B40

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Frączek, Krzysztof

On resonant energy sets for Hamiltonian systems with reflections. arXiv:2405.14464

Preprint, arXiv:2405.14464 [math.DS] (2024).

MSC: 37E35 37C83 37J12 34L25 34C15 70K28 70K30

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Diaz, Inti Cruz

An Algorithmic Classification of Generalized Pseudo-Anosov Homeomorphisms via Geometric Markov Partitions. arXiv:2405.07954

Preprint, arXiv:2405.07954 [math.DS] (2024).

MSC: 37E30 37C86 37C83 37C15 37B10

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Diaz, Inti Cruz

A classification of pseudo-Anosov homeomorphisms via geometric Markov partitions. arXiv:2405.06160

Preprint, arXiv:2405.06160 [math.DS] (2024).

MSC: 37B10 37C15 37C83 37C86 37E30

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Bálint, Péter; Terhesiu, Dalia

Generalized law of iterated logarithm for the Lorentz gas with infinite horizon. arXiv:2403.19582

Preprint, arXiv:2403.19582 [math.PR] (2024).

MSC: 37A50 37D50 37A60 60F15 60F17

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Hwang, Zaijong; Marx, Christoph A.; Seaward, Joseph J.; Jitomirskaya, Svetlana; Olshanii, Maxim

Growth of the Wang-Casati-Prosen counter in an integrable billiard. (English) Zbl 07901057

SciPost Phys. 14, No. 2, Paper No. 17, 16 p. (2023).

MSC: 37C83 37A25 37J35 70K55 37M25

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Glutsyuk, Alexey

Density of a thin film billiard reflection pseudogroup in a Hamiltonian symplectomorphism pseudogroup. (English) Zbl 1547.53105

Isr. J. Math. 258, No. 1, 137-184 (2023).

Reviewer: William J. Satzer Jr. (St. Paul)

MSC: 53D22 17B66 37J39 37J11 37C83

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Fomenko, A. T.

Billiards of variable configuration and billiards with slipping in Hamiltonian geometry and topology. (English) Zbl 1546.37101

Lobachevskii J. Math. 44, No. 10, 4512-4522 (2023).

MSC: 37J35 37J39 37C83 70E40

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Fomenko, Anatoly T.; Vedyushkina, Viktoriya V.

Billiards and integrable systems. (English. Russian original) Zbl 1541.37029

Russ. Math. Surv. 78, No. 5, 881-954 (2023); translation from Usp. Mat. Nauk 78, No. 5, 93-176 (2023).

MSC: 37C83 37J35 37J39 37J20 53D25 37D40

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Morelli, Juan C.

Erratum to: “A persistently singular map of \(\mathbb{T}^{n}\) that is \(C^{1}\) robustly transitive”. (Erratum à : Une application \(C^{1}\) robustement transitive dans \(\mathbb{T}^{n}\) avec singularités persistantes.) (English) Zbl 1539.37029

Bull. Soc. Math. Fr. 151, No. 3, 435-436 (2023).

MSC: 37C20 57R45 57N16

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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

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Shamolin, M. V.

Invariants of fifth-order homogeneous systems with dissipation. (English. Russian original) Zbl 1535.37071

Dokl. Math. 108, No. 3, 506-513 (2023); translation from Dokl. Ross. Akad. Nauk, Mat. Inform. Protsessy Upr. 514, No. 1, 98-106 (2023).

MSC: 37J35 37C79 70H06

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de Rezende, Ketty A.; Grulha, Nivaldo G. jun.; Lima, Dahisy V. de S.; Zigart, Murilo A. J.

Conley index theory for Gutierrez-Sotomayor flows on singular 3-manifolds. (English) Zbl 1539.37022

Topol. Methods Nonlinear Anal. 62, No. 1, 267-326 (2023).

MSC: 37B30 37B25 57N80 58K45 57R65

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Godoy, Yamile; Harrison, Michael; Salvai, Marcos

Tangent ray foliations and their associated outer billiards. (English) Zbl 1544.37019

Rev. Mat. Iberoam. 39, No. 6, 2349-2369 (2023).

Reviewer: Jesus Muciño Raymundo (Morelia)

MSC: 37C86 37C83 37D40 53D10

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Artemova, Elizaveta Markovna

Dynamics of two vortices on a finite flat cylinder. (Russian. English summary) Zbl 07806967

Vestn. Udmurt. Univ., Mat. Mekh. Komp’yut. Nauki 33, No. 4, 642-658 (2023).

MSC: 76B47 70H05 37Jxx 34Cxx 37C79

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Kuznetsova, A. A.

Modeling the degenerate singularities of integrable billiard systems by billiard books. (English. Russian original) Zbl 1537.37065

Mosc. Univ. Math. Bull. 78, No. 5, 207-215 (2023); translation from Vestn. Mosk. Univ., Ser. I 78, No. 5, 3-10 (2023).

MSC: 37J35 37J39 37C83

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Pustovoitov, S. E.

Classification of singularities of the Liouville foliation of an integrable elliptical Billiard with a potential of fourth degree. (English) Zbl 1533.37122

Russ. J. Math. Phys. 30, No. 4, 643-673 (2023).

MSC: 37J39 37J35 37C83

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Minenkov, D. S.; Sergeev, S. A.

Asymptotics of the whispering gallery-type in the eigenproblem for the Laplacian in a domain of revolution diffeomorphic to a solid torus. (English) Zbl 1536.81057

Russ. J. Math. Phys. 30, No. 4, 599-620 (2023).

MSC: 81Q15 81P45 35P15 35J05 30D40 33C10 37C83 81Q80

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Akpan, D.; Oshemkov, A.

Elementary differential singularities of three-dimensional Nijenhuis operators. (English) Zbl 1533.37143

Russ. J. Math. Phys. 30, No. 4, 425-431 (2023).

MSC: 37K25 58K45 53B20

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Filipuk, Galina; Stokes, Alexander

On Hamiltonian structures of quasi-Painlevé equations. (English) Zbl 1533.34069

J. Phys. A, Math. Theor. 56, No. 49, Article ID 495205, 37 p. (2023).

Reviewer: Yousuke Ohyama (Tokushima)

MSC: 34M55 34M35 37J65

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Kryzhevich, Sergey; Plakhov, Alexander

Billiard in a rotating half-plane. (English) Zbl 1545.37027

J. Dyn. Control Syst. 29, No. 4, 1695-1707 (2023).

Reviewer: Yulianna Perepelkina (Moskva)

MSC: 37C83 37N05 70F25 70F35

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Chen, Jianyu; Wang, Fang; Zhang, Hong-Kun

Inducing schemes with finite weighted complexity. (English) Zbl 1542.37023

J. Stat. Phys. 190, No. 12, Paper No. 195, 26 p. (2023).

Reviewer: Xu Zhang (Weihai)

MSC: 37D35 37C83 37D40

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Osterman, Otto Vaughn

On length spectrum rigidity of dispersing billiard systems. (English) Zbl 1544.37018

J. Mod. Dyn. 19, 847-878 (2023).

MSC: 37C83 37C27 37J46

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Bobrova, I. A.

Different linearizations of non-abelian second Painlevé systems and related monodromy surfaces. (English) Zbl 1531.37059

J. Math. Phys. 64, No. 10, Article ID 101702, 24 p. (2023).

MSC: 37J65 34M55 34M56 34M35

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Sedaghatnia, P.; Hassanabadi, H.; Junker, G.; Křiž, J.; Hassanabadi, S.; Chung, W. S.

Investigation of the generalised Wigner-Dunkl harmonic oscillator and its coherent states. (English) Zbl 1535.81114

Ann. Phys. 458, Part 1, Article ID 169445, 16 p. (2023).

MSC: 81Q12 81R30 42B37 58J47 51F15 37N20

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Found 1,845 Documents (Results 1–100)

The problem of optimal camouflaging. (English) Zbl 07965645

Non-periodic not everywhere dense trajectories in triangular billiards. (English) Zbl 07959106

Convective stability in scalar balance laws. (English) Zbl 07953701

Ivrii’s conjecture for some cases in outer and symplectic billiards. (English) Zbl 07946857

A study of the long-term behavior of hybrid systems with symmetries via reduction and the Frobenius-Perron operator. (English) Zbl 07965862

Superdiffusive limits beyond the Marcus regime for deterministic fast-slow systems. (English) Zbl 07965286

Topological moduli space for germs of holomorphic foliations. III: Complete families. (English) Zbl 07962854

A bifurcation analysis of simple singularities: cones, cross-caps, double and triple crossing points. (English) Zbl 07961193

Normalization of singular contact forms and primitive 1-forms. (English) Zbl 07955881

Periodic trajectories and topology of the integrable Boltzmann system. (English) Zbl 07954885

New cases of integrable ninth-order conservative and dissipative dynamical systems. (English) Zbl 07950004

Orbital invariants of billiards and linearly integrable geodesic flows. (English. Russian original) Zbl 07945686

Compensated integrability on tori; a priori estimate for space-periodic gas flows. (Intégrabilité par compensation sur un tore; estimation a priori pour les écoulements gazeux périodiques en espace.) (English. French summary) Zbl 07945485

Poincaré-Hopf theorem for Filippov vector fields on 2-dimensional compact manifolds. (English) Zbl 07941374

Topology of isoenergy surfaces of billiard books glued of annuli. (English. Russian original) Zbl 07938317

Topological invariants of some ordered billiard games. (English. Russian original) Zbl 07938316

Singularities of 3D vector fields preserving the Martinet form. (English. Russian original) Zbl 07938268

Random circular billiards on surfaces of constant curvature: pseudo integrability and mixing. (English) Zbl 07936999

On the extinction of multiple shocks in scalar viscous conservation laws. (English) Zbl 07935905

Non-density of \(C^0\)-stable mappings on non-compact manifolds. (English) Zbl 07931979

On the role of the surface geometry in convex billiards. (English) Zbl 07930649

Geometric analysis of fast-slow PDEs with fold singularities via Galerkin discretisation. (English) Zbl 07930646

Isomonodromic and isospectral deformations of meromorphic connections: the \(\mathfrak{sl}_2(\mathbb{C})\) case. (English) Zbl 07930635

Bratteli-Vershikisability of polygonal billiards on the hyperbolic plane. (English) Zbl 07929531

Maximal codimension collisions and invariant measures for hard spheres on a line. (English) Zbl 07922461

The Minkowski billiard characterization of the EHZ-capacity of convex Lagrangian products. (English) Zbl 07920496

Integer orbits in rectangular lattice billiards. (English) Zbl 07919072

Measure of maximal entropy for finite horizon Sinai billiard flows. (Mesure d’entropie maximale des flots billards de Sinai à horizon fini.) (English. French summary) Zbl 07914804

Classification of Filippov type 3 singular points in planar bimodal piecewise smooth systems. (English) Zbl 07906736

On the rationality of the Nielsen zeta function for maps on solvmanifolds. (English) Zbl 07903130

Examples of projective billiards with open sets of periodic orbits. (English) Zbl 07901507

Totally integrable symplectic billiards are ellipses. (English) Zbl 07900776

Confocal parabolic billiard with gravitational potential: classical and quantum description. (English) Zbl 07899894

A Lipschitz metric for \(\alpha\)-dissipative solutions to the Hunter-Saxton equation. (English) Zbl 1544.35032

Integrable mechanical billiards in higher-dimensional space forms. (English) Zbl 07888868

Monotone twist maps and Dowker-type theorems. (English) Zbl 07887952

Thermo-elastic and thermo-piezo-elastic interaction crack type boundary-transmission problems with regard to the microrotation. (English) Zbl 1547.35665

Invariants of seventh-order homogeneous dynamical systems with dissipation. (English) Zbl 07883848

Research of the structure of the Liouville foliation of an integrable elliptical billiard with polynomial potential. (Russian. English summary) Zbl 07879124

Deterministic and stochastic surrogate models for a slowly driven fast oscillator. (English) Zbl 1546.34131

Outer billiards in the spaces of oriented geodesics of the three-dimensional space forms. (English) Zbl 07870406

On rationally integrable planar dual multibilliards and piecewise smooth projective billiards. (English) Zbl 1547.37043

On infinitely many foliations by caustics in strictly convex open billiards. (English) Zbl 07861155

Closed orientable surfaces and fold Gauss maps. (English) Zbl 07855801

Rotation functions of integrable billiards as orbital invariants. (English) Zbl 1546.37100

Weights, Kovalevskaya exponents and the Painlevé property. (Poids, exposants de Kovalevskaya et propriété de Painlevé.) (English. French summary) Zbl 07852671

A note on the semiclassical measure at singular points of the boundary of the Bunimovich stadium. (Une note sur la mesure semiclassique aux points singuliers du bord du stade de Bunimovich.) (English. French summary) Zbl 1545.37028

Uniform asymptotic stability for convection-reaction-diffusion equations in the inviscid limit towards Riemann shocks. (English) Zbl 1540.35050

Higher order terms of Mather’s \(\beta\)-function for symplectic and outer billiards. (English) Zbl 1544.37041

Solving the cohomological equation for locally Hamiltonian flows. I: Local obstructions. (English) Zbl 1547.37071

Integrable outer billiards and rigidity. (English) Zbl 1545.37054

Conditional proof of the ergodic conjecture for falling ball systems. (English) Zbl 1542.37008

On the asymptotic growth of Birkhoff integrals for locally Hamiltonian flows and ergodicity of their extensions. (English) Zbl 1542.37003

On the ergodic theory of the real Rel foliation. (English) Zbl 1543.37034

Homoclinic and heteroclinic intersections for lemon billiards. (English) Zbl 1541.37030

Another billiard problem. (English) Zbl 1540.37084

Classical and quantum elliptical billiards: mixed phase space and short-range correlations in singlets and doublets. (English) Zbl 1541.81201

Resonances and weighted zeta functions for obstacle scattering via smooth models. (English) Zbl 1537.37036

Lyapunov exponents and nonadapted measures for dispersing billiards. (English) Zbl 1537.37035

Rates of mixing for the measure of maximal entropy of dispersing billiard maps. (English) Zbl 1536.37006

Rotating rod and ball. (English) Zbl 1536.70016

On differential equations of integrable billiard tables. (English) Zbl 1535.37034

Cusps in heavy billiards. (English) Zbl 1536.37033

Projective integrable mechanical billiards. (English) Zbl 1533.37074

Symmetric periodic orbits in symmetric billiards. (English) Zbl 1533.37073

Non-integrable dynamics. Time-quantitative results. (English) Zbl 07745800

Planar vector fields in the kernel of a 1–form. arXiv:2411.07587

Generalized Poincaré-Dulac singularities of holomorphic foliations. arXiv:2411.02873

Singular points in generic two-parameter families of vector fields on 2-manifold. arXiv:2410.11465

Weak mixing in rational billiards. arXiv:2410.11117

On the Local-Global Conjecture for Combinatorial Period Lengths of Closed Billiards on the Regular Pentagon. arXiv:2409.10682

Magic Billiards: the Case of Elliptical Boundaries. arXiv:2409.03158

Skew-product systems over infinite interval exchange transformations. arXiv:2408.14079