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;



    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)