List of Publications

Papers published in refereed journals:

1. Chaotic and ergodic properties of cylindric billiards;
   
   • Ergodic Theory and Dynamical Sytems, 19 (1999), 1127-1156. (ps, pdf)
2. Multi-dimensional semi-dispersing billiards:singularities and the fundamental theorem;
   
   • joint with Nikolai Chernov, Domokos Szász and Imre Péter Tóth;
   • Annales Henri Poincaré 3 (2002), 451-482. (ps, pdf)
3. Geometry of multi-dimensional dispersing billiards;
   
   • joint with Nikolai Chernov, Domokos Szász and Imre Péter Tóth;
   • Astérisque, 286 (2003) 119-150. (ps, pdf)
4. Correlation decay in certain soft billiards;
   
   • joint with Imre Péter Tóth;
   • Communications in Mathematical Physics, 243 (2003) 55-91. (ps, pdf)
5. Mixing and its rate in soft and hard billiards motivated by the Lorentz process;
   
   • joint with Imre Péter Tóth;
   • Physica D, 187 (2004) 128-135. (ps, pdf)
6. Ergodicity of two hard balls in integrable polygons;
   
   • joint with Serge Troubetzkoy;
   • Nonlinearity, 17 (2004) 2069-2090. (ps, pdf)
7. Rotor interaction in the annulus billiard;
   
   • joint with Serge Troubetzkoy;
   • Journal of Statistical Physics, 117 (2004) 681-702. (ps, pdf)
8. Hyperbolicity in multi-dimensional Hamiltonian sytems with applications to soft billiards;
   
• joint with Imre Péter Tóth;
  
• Discrete and Continuous Dynamical Systems, Series A, 15 (2006) 37-59. (ps, pdf)
9. Limit theorems in the stadium billiard;
   
   • joint with Sébastien Gouëzel;
   • Communications in Mathematical Physics, 263 (2006) 461-512. (ps, pdf)
10. On the zero mass limit of tagged particle diffusion in the 1-d Rayleigh gas;
    
    • joint with Bálint Tóth and Imre Péter Tóth;
      
    • Journal of Statistical Physics, 127 (2007) 657-675. (ps, pdf)
11. Local ergodicity for systems with growth properties including multi-dimensional dispersing billiards;
    
    • joint with Pavel Bachurin and Imre Péter Tóth;
      
    • Israel Journal of Mathematics, 167 (2008) 155-176. (ps, pdf)
12. Exponential decay of correlations in multi-dimensional dispersing billiards;
    
    • joint with Imre Péter Tóth;
      
    • Annales Henri Poincaré, 9 (2008) 1309-1369. (ps, pdf)
13. Decay of correlations and invariance principles for dispersing billiards with cusps, and related planar billiard flows;
    
    • joint with Ian Melbourne;
      
    • Journal of Statistical Physics, 133 (2008) 435-447. (ps, pdf)
14. Ergodicity and Energy Distributions for some Boundary Driven Integrable Hamiltonian Chains;
    • joint with Kevin K. Lin and Lai-Sang Young;
    • Communications in Mathematical Physics, 294 (2010) 199–228.  (ps, pdf)
15. Chaos and stability in a two-parameter family of convex billiard tables;
    • joint with Miklós Halász, Jorge Hernández-Tahuilán and David P. Sanders;
    • Nonlinearity, 24 (2011) 1499-1521 ( pdf)
16. Limit theorems for dispersing billiards with cusps;
    • joint with Nikolai Chernov and Dmitry Dolgopyat;
    • Communications in Mathematical Physics, 308 (2011) 479-510( pdf)
17. Example for Exponential Growth of Complexity in a Finite Horizon Multi-dimensional Dispersing Billiard;
    
    • joint with Imre Péter Tóth;
    • Nonlinearity, to appear (pdf)
18. Statistical properties of the system of two falling balls;
    
    • joint with Gábor Borbély and András Némedy Varga;
    • Chaos, to appear ( pdf)



Preprints:

19. Decay of correlations for flows with unbounded roof function, including the infinite horizon planar periodic Lorentz gas;
    • joint with Ian Melbourne;
    • ( pdf)


20. Convergence of moments for dispersing billiards with cusps;
    
    • joint with Nikolai Chernov and Dmitry Dolgopyat;
    • (pdf)



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);
   
   • (pdf)
2. Halász Miklós diplomamunkája (in Hungarian);
   
   • (pdf)
3. MSc thesis by András Némedy Varga;
   
   • (pdf)
4. BSc thesis by Gábor Borbély;
   
   • (pdf)
5. TDK thesis by Gábor Borbély  (TDK = association for research of undergraduate students) 
   
   • (pdf)