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  • 1
    Electronic Resource
    Electronic Resource
    Lagrangian flows: The dynamics of globally minimizing orbits (1997)
    Springer
    Bulletin of the Brazilian Mathematical Society 28 (1997), S. 141-153 
    Details
    ISSN: 1678-7714
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The objective of this note is to present some results, to be proved in a forthcoming paper, about certain special solutions of the Euler-Lagrange equations on closed manifolds. Our main results extend to time dependent periodic Lagrangians with minor modifications. We have chosen the autonomous case because this formally simpler framework allows to reach more easily the core of our concepts and results. Moreover the autonomous case exhibits certain special features involving the energy as a first integral that deserve special attention. They are closely related to the link found by Carneiro [C] between the energy and Mather's action function [Ma].
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01233389
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    On a theorem of Fatou (1993)
    Springer
    Bulletin of the Brazilian Mathematical Society 24 (1993), S. 1-11 
    Details
    ISSN: 1678-7714
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We prove a result on the backward dynamics of a rational function nearby a point not contained in the ω-limit set of a recurrent critical point. As a corollary we show that a compact invariant subset of the Julia set, not containing critical or parabolic points, and not intersecting the ω-limit set ofrecurrent critical points, is expanding, thus extending a classical criteria of Fatou. We also prove that the boundary of a Siegel disk is always contained in the ω-limit set of arecurrent critical point.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01231694
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  • 3
    Electronic Resource
    Electronic Resource
    Hyperbolicity, sinks and measure in one dimensional dynamics (1985)
    Springer
    Communications in mathematical physics 100 (1985), S. 495-524 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract Letf be aC 2 map of the circle or the interval and letΣ(f) denote the complement of the basins of attraction of the attracting periodic orbits. We prove thatΣ(f) is a hyperbolic expanding set if (and obviously only if) every periodic point is hyperbolic andΣ(f) doesn't contain the critical point. This is the real one dimensional version of Fatou's hyperbolicity criteria for holomorphic endomorphisms of the Riemann sphere. We also explore other applications of the techniques used for the result above, proving, for instance, that for everyC 2 immersionf of the circle (i.e. a map of the circle onto itself without critical points), either its Julia set has measure zero or it is the whole circle and thenf is ergodic, i.e. positively invariant Borel sets have zero or full measure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01217727
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  • 4
    Electronic Resource
    Electronic Resource
    Hyperbolicity, sinks and measure in one dimensional dynamics (1987)
    Springer
    Communications in mathematical physics 112 (1987), S. 721-724 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01225382
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  • 5
    Electronic Resource
    Electronic Resource
    Absolute stability and bifurcation theory (1979)
    Springer
    Inventiones mathematicae 53 (1979), S. 59-75 
    Details
    ISSN: 1432-1297
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01403191
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  • 6
    Electronic Resource
    Electronic Resource
    On the instability of Herman rings (1985)
    Springer
    Inventiones mathematicae 81 (1985), S. 459-471 
    Details
    ISSN: 1432-1297
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01388582
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  • 7
    Electronic Resource
    Electronic Resource
    Invariant sets of Anosovs diffeomorphisms (1978)
    Springer
    Inventiones mathematicae 46 (1978), S. 147-152 
    Details
    ISSN: 1432-1297
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01393252
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  • 8
    Book
    Book
    Ergodic theory and differentiable dynamics; 8 (1987)
    Berlin u.a. :Springer,
    Details
    Title: Ergodic theory and differentiable dynamics; 8
    Author: Mane, Ricardo
    Publisher: Berlin u.a. :Springer,
    Year of publication: 1987
    Pages: 317 S.
    Series Statement: Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge 8
    Type of Medium: Book
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