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  • 1
    Electronic Resource
    Electronic Resource
    Geometry of geometrically finite one-dimensional maps (1993)
    Springer
    Communications in mathematical physics 156 (1993), S. 639-647 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study the geometry of certain one-dimensional maps as dynamical systems. We prove the property of bounded and bounded nearby geometry of certainC 1+α one-dimensional maps with finitely many critical points. This property enables us to give the quasisymmetric classification of geometrically finite one-dimensional maps.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02096866
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  • 2
    Electronic Resource
    Electronic Resource
    Expanding direction of the period doubling operator (1992)
    Springer
    Communications in mathematical physics 144 (1992), S. 509-520 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We prove that the period doubling operator has an expanding direction at the fixed point. We use the induced operator, a “Perron-Frobenius type operator,” to study the linearization of the period doubling operator at its fixed point. We then use a sequence of linear operators with finite ranks to study this induced operator. The proof is constructive. One can calculate the expanding direction and the rate of expansion of the period doubling operator at the fixed point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099180
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  • 3
    Electronic Resource
    Electronic Resource
    Asymptotic differentiable structure on Cantor set (1993)
    Springer
    Communications in mathematical physics 155 (1993), S. 503-509 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We study hyperbolic maps depending on a parameter ε. Each of them has an invariant Cantor set. As ε tends to zero, the map approaches the boundary of hyperbolicity. We analyze the asymptotics of scaling function of the invariant Cantor set as ε goes to zero. We show that there is a limiting scaling function of the limiting map and this scaling function has dense jump discontinuities because the limiting map is not expanding. Removing these discontinuities by continuous extension, we show that we obtain the scaling function of the limiting map with respect to a Ulam-von Neumann type metric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02096725
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    On Ulam-von Neumann transformations (1995)
    Springer
    Communications in mathematical physics 172 (1995), S. 449-459 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We define and study Ulam-von Neumann transformations which are certain interval mappings and conjugate toq(x)=1−2x 2 on [−1,1]. We use a singular metric on [−1,1] to study a Ulam-von Neumann transformation. This singular metric is universal in the sense that it does not depend on any particular mapping but only on the exponent of this mapping at its unique critical point. We give the smooth classification of Ulam-von Neumann transformations by their eigenvalues at periodic points and exponents and asymmetries.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02101803
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  • 5
    Electronic Resource
    Electronic Resource
    Markov partitions and Feigenbaum-like mappings (1995)
    Springer
    Communications in mathematical physics 171 (1995), S. 351-363 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We construct a Markov partition for a Feigenbaum-like mapping. We prove that this Markov partition has bounded nearby geometry property similar to that for a geometrically finite one-dimensional mappings [8]. Using this property, we give a simple proof that any two Feigenbaum-like mappings are topologically conjugate and the conjugacy is quasisymmetric.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02099274
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  • 6
    Electronic Resource
    Electronic Resource
    A Proof of the Existence and Simplicity of a Maximal Eigenvalue for Ruelle–Perron–Frobenius Operators (1999)
    Springer
    Letters in mathematical physics 48 (1999), S. 211-219 
    Details
    ISSN: 1573-0530
    Keywords: locally expanding ; mixing ; Ruelle–Perron–Frobenius operator ; maximal eigenvalue
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We give a new proof of a result due to Ruelle about the existence and simplicity of a unique maximal eigenvalue for a Ruelle–Perron–Frobenius operator acting on some Hölder continuous function space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1007595323704
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    Paper (German National Licenses)
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