Research Interests MSC2000

Dynamical Systems and Ergodic Theory (in particular Thermodynamic Formalism and Dimension Theory 37C45, 37D35, 28D20, 37D40), Nonuniformly Hyperbolic Dynamics (37D,37E05), Differential Equations (Averaging Methods, Stability Theory and Strange Attractors)

Dynamical Systems and Ergodic Theory:

Hausdorff Dimension Estimates by Use of a Tubular Caratheodory Structure and Their Application to Stability Theory. (with G.A. Leonov and V. Reitmann),
Nonlinear Dyn. Syst. Theory 1 (2001) 2, 169-192. [pdf]

Maximum Local Lyapunov Dimension Bounds the Box Dimension. Direct Proof for Invariant Sets on Riemannian Manifolds.
Z. Anal. Anw. 22 (2003) 3, 553-568. [ps, pdf]

Lower bounds for the topological entropy.
Discrete Contin. Dyn. Syst. 12 (2005) 3, 555-565. [ps, pdf]

Dimension estimates beyond conformal and hyperbolic dynamics.
Dynamical Systems 20 (2005) 2, 267-280. [ps, pdf]

Multifractal analysis for Lyapunov exponents on nonconformal repellers. (with L. Barreira)
Commun. Math. Phys. 267 (2006) 2, 393-418. [pdf]

Topological pressure via periodic points. (with Ch. Wolf)
Trans. Amer. Math. Soc. 360 (2008), 545-561. [math.DS/0509630]

Topological pressure for one-dimensional holomorphic dynamical systems. (with Ch. Wolf)
Bulletin Polish Acad. Sci. Math. 55 (2007), 53-62. [math.DS/0705.4572]

Geometry of limit sets for expansive Markov systems. (with M. Rams)
Trans. Amer. Math. Soc. 361 (2009), 2001-2020. [math.DS/0705.1040]

The Lyapunov spectrum of some parabolic systems. (with M. Rams)
Ergodic Theory Dynam. Systems 29 (2009), 919-940. math.DS/0709.2832]

Equality of pressures for diffeomorphisms preserving hyperbolic measures.
Mathematische Zeitschrift 261 (2009), 711-724. [math.DS/0803.1525]

On the distribution of periodic orbits. (with Ch. Wolf)
Preprint. [math.DS/0901.2139]

On the Lyapunov spectrum for rational maps. (with F. Przytycki and M. Rams)
Preprint. [math.DS/0809.3363]

Expanding repellers for non-uniformly expanding maps with singularities and criticalities.
Preprint.

(Non)Invariance of dynamical quantities for orbit equivalent flows. (with A. Motter)
Preprint.



Nonlinear Dynamics and Statistical Physics:

with W. Just, N. Baba, A. Riegert and H. Kantz
Elimination of fast chaotic degrees of freedom: On the accuracy of the Born approximation.
Journal of Statistical Physics 112 (2003) 1/2, 277-292. [ps, pdf]

with H. Kantz, W. Just, N. Baba and A. Riegert
Fast chaos versus white noise: entropy analysis and a Fokker Planck model for the slow dynamics.
Physica D: Nonlinear Phenomena 187 (2004) 1-4, 200-213. [ps, pdf]

with H. Kantz, W. Just, N. Baba and A. Riegert
Hamiltonian chaos acts like a finite energy reservoir: Accuracy of the Fokker-Planck approximation.
Phys. Rev. Lett. 94 (2005) 054103.

with H. Kantz
Dynamical quantities and their numerical analysis by saddle periodic orbits
Pysica D: Nonlinear Phenomena 232 (2007) 166-172.

with A. Motter
Time-metric equivalence and dimension jump in nonlinear dynamical systems
Physical Review E. 79 (2009) 065202(R).





Communications in conferences:

Hausdorff dimension estimates by use of adapted Caratheodory outer measures and applications to invariant sets with an equivariant tangent bundle splitting.
Equadiff 99, World Scientific, 2000, pp. 665-667.

Lower bounds of the topological entropy.
Progress in analysis, Vol. I, II (Berlin, 2001), 535-543, World Sci. Publishing, River Edge, NJ, 2003.