HomePage of Maciej P. Wojtkowski

My papers:

• A simple proof of polar decomposition in pseudo-Euclidean geometry . . .
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  Abstract   We give a simple direct proof of the polar decomposition for separated linear maps in pseudo-Euclidean geometry. (published in Fund. Math. 206(2009), 299 -306)
  
  
  • A family of pseudo-Anosov maps . . .
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    Abstract   We study a family of area-preserving maps of the 2-torus and show that they are pseudo-Anosov. We present a method to construct finite Markov partitions for this family which utilizes their common symmetries. Through these partitions we show explicitly that each map is a tower over a first return map, intimately linked to a toral automorphism. This enables us to calculate directly some dimensional characteristics of the dynamics. (published in Nonlinearity 22(2009), 1743 - 1760)
    
    
    • Abstract fluctuation theorem . . .
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      Abstract   We formulate an abstract fluctuation theorem which sheds light on mathematical relations between the fluctuation theorems of Bochkov- Kuzovlev, [B-K], and Jarzynski, [J], on one hand and those of Evans- Searles, [E-S], and Gallavotti-Cohen, [G-C], on the other. (published in Ergodic Theory and Dynamical Systems 29 (2009), 273 - 279)
      
      
      • Geometry of Kalman filters . . .
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        Abstract   We present a geometric explanation of Kalman filters in terms of a symplectic linear space and a special quadratic form on it. It is an extension of the work of Bougerol \cite{B1} with application of a different metric introduced in \cite{L-W}. The new results are contained in Theorems 1 and 4.
        
        
        • Gaussian thermostats as geodesic flows of nonsymmetric linear connections . . .
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          Abstract   We establish that Gaussian thermostats are geodesic flows of special metric connections. We give sufficient conditions for hyperbolicity of geodesic flows of metric connections in terms of their curvature and torsion.
          
          

        • Design of hyperbolic billiards . . .
          pdf file: 251732 bytes Abstract   We formulate a general framework for the construction of hyperbolic billiards. Spherical symmetry is exploited for a simple treatment of billiards with spherical caps and soft billiards in higher dimensions. Other examples include the Papenbrock stadium.
          
          

        • Hyperbolic billiards . . .
          pdf file: 110445 bytes Abstract   Published in the Encyclopedia of Mathematical Physics, (eds. Francoise, Naber, Tsou, Elsevier 2006.
          
          

        • Rigidity of some Weyl manifolds with nonpositive sectional curvature . . .
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          Abstract   We provide a list of all locally metric Weyl connections with nonpositive sectional curvatures on two types of manifolds, n-dimensional tori $\Bbb T^n$ and $\Bbb M^n =\Bbb S^1\times\Bbb S^{n-1}$ with the standard conformal structures. For $\Bbb M^n$ we prove that it carries no other Weyl connections with nonpositive sectional curvatures, locally metric or not. For $\Bbb T^n$ we prove the same in the more narrow class of integrable connections.