List of Publications
Imre Péter Tóth
March 2013
A magyar változat itt található.
Every completed publication can be downloaded from this page.
In preparation
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Generalized Hölder continuity and oscillation functions;
manuscript;
abstract
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An expansion estimate for dispersing planar billiards with corner points;
joint with Jacopo de Simoi; submitted; Arxiv preprint arXiv:1212.6897
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Entropy and Hausdorff Dimension of the Branching Measure in General Branching Processes;
joint with Anna Rudas; in preparation; manuscript
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Bounded complexity of singularities in typical planar dispersing billiards; in preparation
Papers in refereed international journals
The final or almost final manuscript can be downloaded from here
in pdf.
Some papers can also be dowloaded from the server of the publisher.
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Entropy and Hausdorff Dimension in Random Growing Trees;
joint with Anna Rudas; Stochastics and Dynamics, 13, 1250010 (2013); Arxiv preprint arXiv:1004.0977;
manuscript
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Example for Exponential Growth of Complexity in a Finite Horizon Multi-dimensional Dispersing Billiard;
joint with Péter Bálint; Nonlinearity 25 1275 (2012); manuscript
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Billiard Models and Energy Transfer; joint with Zsolt Pajor-Gyulai and Domokos Szász; Proc. of International Congress on Math. Physics held in Prague, 2009, pp. 6. World Scientific.
manuscript;
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Exponential Decay of Correlations in Multi-dimensional Dispersing
Billiards;
joint with Péter Bálint;
Annales Henri Poincaré 9(7) 1309-1369 (2008).
manuscript;
abstract
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Local ergodicity for systems with growth properties including
multi-dimensional dispersing billiards;
joint with Pavel Bachurin and Péter Bálint;
Israel Journal of Mathematics 167 155-176 (2008).
manuscript;
abstract
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On the zero mass limit of tagged particle diffusion in the 1-d
Rayleigh gas;
joint with Péter Bálint and Bálint Tóth;
Journal of Statistical Physics 127 657-675 (2007).
manuscript;
abstract
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Hyperbolicity in multi-dimensional Hamiltonian sytems
with applications to soft billiards;
joint with Péter Bálint;
Discrete and Continuous Dynamical Systems, Series A 15 37-59 (2006).
manuscript;
abstract
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Correlation Decay in certain soft billiards,
joint with Péter Bálint;
Communications in Mathematical Physics 243 55-91 (2003).
manuscript;
abstract;
download from the publisher
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Mixing and its rate in `soft' and `hard' billiards motivated by the Lorentz process;
joint with Péter Bálint;
Physica D 187 128-135 (2004).
manuscript;
abstract;
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Multidimensional Semi-Dispersing Billiards:
Singularities and the Fundamental Theorem;
joint with Péter Bálint, Nikolai Chernov and Domokos Szász;
Annales Henry Poincaré 3 451-482 (2002).
manuscript;
abstract;
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Geometry of Multidimensional Dispersing Billiards;
joint with Péter Bálint, Nikolai Chernov and Domokos Szász;
Astérisque 286 119-150 (2003).
manuscript;
abstract;
Diploma thesis, PhD thesis
Students' work
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Róbert Sepsi: Számítógépes szimulációk megbízhatósága; (Reliability of computer simulations)
BSc diploma thesis (in Hungarian); Technical University of Buapest, Department of Mathematics (2009).
download (pdf)
Open problems in Billiards
attempt to collect today's problems of Billiards Theory
into an on-line database
(joint with Péter Bálint and Domokos Szász);
link
Material appeared in conference-printouts
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Hyperbolicity in Multi-dimensional Soft Billiards;
summary of talk at the workshop
Applied Mathematics and Computational Physics
(Göd, Hungary, 30 April -- 1 May 2004).
download
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Correlation Decay in Billiards;
summary of talk at the workshop
Applied Mathematics and Computational Physics
(Göd, Hungary, 12-13 April 2003);
joint with Péter Bálint.
download
Teaching
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Proposal for the detailed practice course material
and exercises of the subject ``Mathematics A1'';
(2006) (in Hungarian).
download
Material of numerical investigations
The items here are roughly documented programs and
results obtained from them. Most documentation is in Hungarian.
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Simulation of the diffusion coefficient in a Gaspard-Gilbert model with weak interaction force;
(2009). The description can be found in the README file.
link
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Simulation of correlation decay in cylindric billiards;
(2007). The description can be found in the README file.
link
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Correlation decay of the function f(x)=3x (mod 1) on a lattice;
(2006). The description can be found in the source file triple.c .
link
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Simulation of correlation decay in stadium-like billiards;
(2005). The description can be found in the README file.
link
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Numerical investigation of scattering on circularly symmetric
potentials in connection with correlation decay of soft
billiards;
(2004). Description in the file _Readme.txt .
link
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numerical investigation of the inversion number of cycles ;
(2004). Description in the file _Readme.txt .
link
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Spectrum of the invariant measure for a random iterated
function system;
(2001). Description in the file sorba.ps .
link