List of Publications


Papers published/to appear in refereed journals:


  1. Chaotic and ergodic properties of cylindric billiards;
  2. Multi-dimensional semi-dispersing billiards:singularities and the fundamental theorem;
  3. Geometry of multi-dimensional dispersing billiards;
  4. Correlation decay in certain soft billiards;
  5. Mixing and its rate in soft and hard billiards motivated by the Lorentz process;
  6. Ergodicity of two hard balls in integrable polygons;
  7. Rotor interaction in the annulus billiard;
  8. Hyperbolicity in multi-dimensional Hamiltonian sytems with applications to soft billiards;
  9. Limit theorems in the stadium billiard;
  10. On the zero mass limit of tagged particle diffusion in the 1-d Rayleigh gas;
  11. Local ergodicity for systems with growth properties including multi-dimensional dispersing billiards;
  12. Exponential decay of correlations in multi-dimensional dispersing billiards;
  13. Decay of correlations and invariance principles for dispersing billiards with cusps, and related planar billiard flows;
  14. Ergodicity and Energy Distributions for some Boundary Driven Integrable Hamiltonian Chains;
  15. Chaos and stability in a two-parameter family of convex billiard tables;
  16. Limit theorems for dispersing billiards with cusps;
  17. Example for Exponential Growth of Complexity in a Finite Horizon Multi-dimensional Dispersing Billiard;
  18. Statistical properties of the system of two falling balls;
  19. The flow of two falling balls mixes rapidly;
  20. Mean-field coupling of identical expanding circle maps;
  21. On the limiting Markov process of energy exchanges in a rarely interacting ball-piston gas;
  22. Convergence of moments for dispersing billiards with cusps;
  23. Equidistribution for standard pairs in planar dispersing billiard flows;
  24. Stability of the invariant distribution for a class of globally coupled maps;
  25. Statistical properties for flows with unbounded roof function, including the Lorenz attractor;
  26. Polynomial decay of correlations for flows, including Lorentz gas examples;
  27. Marked length spectrum, homoclinic orbits and the geometry of open dispersing billiards;
  28. What mathematical billiards teach us about statistical physics?
  29. Periodic Lorentz gas with small scatterers;
  30. An evolution model for polygonal tesselations as models for crack networks and other natural patterns

       

        Preprints:  

    Conference proceedings:

    1. Singularities and mixing porperties of certain hyperbolic billiard systems;
      • joint with Imre Péter Tóth;
      • in Proceedings of the Conference Equadiff 2007, beküldve
    2. Tagged particle diffusion in deterministic dynamics – old and new results;
      • joint with Bálint Tóth and Imre Péter Tóth;
      • in Oberwolfach Research Reports No. 42/2007, (2007)
    3. Singularities and mixing in multi-dimensional dispersing billiards;
      • joint with Imre Péter Tóth;
      • in Oberwolfach Research Reports No. 33/2007, (2007)
    4. An Application of Young's Tower Method: Exponential Decay of Correlations in Multidimensional Dispersing Billiards;
      • joint with Imre Péter Tóth;
      • ESI Preprint 2084, (2008)

    Supervised works:

    1. Halász Miklós TDK dolgozata (in Hungarian);
    2. Halász Miklós diplomamunkája (in Hungarian);
    3. MSc thesis by András Némedy Varga;
    4. BSc thesis by Gábor Borbély;
    5. TDK thesis by Gábor Borbély  (TDK = association for research of undergraduate students) 
    6. PhD thesis of Fanni M. Sélley
    7. BSc thesis of Ádám Bernát
    8. TDK thesis of Ádám Bernát
    9. BSc thesis of Gergő Dénes