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  • 1
    Electronic Resource
    Electronic Resource
    Eine bemerkung zur topologischen entropie (1978)
    Springer
    Monatshefte für Mathematik 85 (1978), S. 177-183 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study fractional quadratic transformationsT of the sphere and try to determine their topological entropy. In the case whereT is a constant mapping or a homeomorphism, the topological entropy is of course zero. In the other cases, we have the following results. IfT has only one fixed point, its entropy is log 2. IfT has exactly two fixed points, it can be written asT z =z−z −1 +v, and ifv is real, then the entropy ofT is again log 2. A general result ofMisiurewicz andPrzytycki shows that the entropy ofT is at least log2, and we conjecture that this entropy is always equal to log2 in the remaining cases, i. e. two fixed points andv not real, and three fixed points.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01534860
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  • 2
    Electronic Resource
    Electronic Resource
    Almost-topological representation theorems for dynamical systems (1979)
    Springer
    Monatshefte für Mathematik 87 (1979), S. 93-108 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For topological dynamical systems (X, T) representation theorems into shift dynamical systems are proved where the representing map φ is a homeomorphism between residual sets. φ can be endowed with additional properties so that the entropies of a measurem and its transport φm are arbitrary close.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01305909
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  • 3
    Electronic Resource
    Electronic Resource
    On strict ergodicity (1973)
    Springer
    Mathematische Zeitschrift 134 (1973), S. 231-253 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01214097
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  • 4
    Electronic Resource
    Electronic Resource
    On unitary operators inducing measure-preserving transformations (1978)
    Springer
    Mathematische Zeitschrift 160 (1978), S. 163-172 
    Details
    ISSN: 1432-1823
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01214266
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  • 5
    Electronic Resource
    Electronic Resource
    The central limit theorem for random perturbations of rotations (1998)
    Springer
    Probability theory and related fields 111 (1998), S. 1-16 
    Details
    ISSN: 1432-2064
    Keywords: Mathematics Subject Classification (1991): 60F05 ; 28D05 ; 58F11
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary. We prove a functional central limit theorem for stationary random sequences given by the transformations on the two-dimensional torus. This result is based on a functional central limit theorem for ergodic stationary martingale differences with values in a separable Hilbert space of square integrable functions.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004400050160
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  • 6
    Electronic Resource
    Electronic Resource
    A short proof of a theorem of Ruelle (1989)
    Springer
    Monatshefte für Mathematik 108 (1989), S. 295-299 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Using the existence of conformal measures in the sense ofSullivan [4] andDenker, Urbański [2] we give a simple proof of Ruelle's Theorem, that the Hausdorff dimension of a hyperbolic Julia set is the solution of the equationP(R,−tlog|R′|)=0.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01501131
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  • 7
    Electronic Resource
    Electronic Resource
    Some new examples of Gibbs measures (1990)
    Springer
    Monatshefte für Mathematik 109 (1990), S. 49-62 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate Gibbs measures on general subshifts. In particular we show the uniqueness of Gibbs measures as equilibrium states and we construct such measures on other spaces than mixing subshifts of finite type or sofic systems.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01298852
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  • 8
    Electronic Resource
    Electronic Resource
    A bounded law of the iterated logarithm for Hilbert space valued martingales and its application to U-statistics (1986)
    Springer
    Probability theory and related fields 72 (1986), S. 111-131 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A bounded law of the iterated logarithm for martingales with values in a separable Hilbert space H is proved. It is then applied to prove invariance principles for U-statistics for independent identically distributed (ℝ-valued) random variables {X j , j≧1} and a kernel h: ℝ m →H, m≧2, which is degenerate for the common distribution function of X j , j≧1. This extends to general m results of an earlier paper on this subject and even gives new results in the case H=ℝ.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00343899
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  • 9
    Electronic Resource
    Electronic Resource
    On U-statistics and v. mise’ statistics for weakly dependent processes (1983)
    Springer
    Probability theory and related fields 64 (1983), S. 505-522 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary Some probabilistic limit theorems for Hoeffding's U-statistic [13] and v. Mises' functional are established when the underlying processes are not necessarily independent. We consider absolutely regular processes [24] and processes (X n)n≧1 which are uniformly mixing [14] as well as their time reversal (X −n )n≦−1, called uniformly mixing in both directions of time. Many authors have weakened the hypothesis of independence in statistical limit theorems and considered m-dependent, Markov or weakly dependent processes; in particular for U statistics under weak dependence Sen [22] has considered *-mixing processes and derived a central limit theorem and a law of the iterated logarithm, while Yoshihara [26] proved central limit theorems and a.s. results in the absolutely regular and uniformly mixing case. Here we extend these results considerably and prove central limit theorems and their rate of convergence (in the Prohorov metric and a Berry Esseén type theorem), functional central limit theorems and a.s. approximation by a Brownian motion. Extensions to multisample versions and other extensions are briefly discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00534953
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  • 10
    Electronic Resource
    Electronic Resource
    Finitary codes and the law of the iterated logarithm (1980)
    Springer
    Probability theory and related fields 52 (1980), S. 321-331 
    Details
    ISSN: 1432-2064
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary We investigate the validity of the law of the iterated logarithm for processes which are obtained from mixing processes via finitary codes with finite moments of order greater than one.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00538896
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