Now showing items 1-8 of 8

  • An example on Lyapunov stability and linearization 

    Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2020-01-01)
    Article
    Restricted access - publisher's policy
    The purpose of this paper is to present an example of a (in the Fréchet sense) discrete dynamical system in a infinite-dimensional separable Hilbert space for which the origin is an exponentially asymptotically stable ...
  • An invertible contraction that is not C<sup>1</sup>-linearizable 

    Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2004)
    Article
    Open Access
    We present an example of a smooth invertible contraction in aninfinite-dimensional Hilbert space that is not locally ${\mathcalC}^{1}$-linearizable near its fixed point.
  • A note on the relationship between spectral radius and norms of bounded linear operators 

    Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2009)
    Article
    Open Access
    Let X be a Banach space and L ( X ) be the Banach algebra of bounded operators on X . In this note we prove that if we have a compact subset K of a commutative sub-algebra of L ( X ), and given " > 0, then ...
  • A result on class-C1 linearization of contractions in infinite dimensions 

    Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2002)
    Article
    Open Access
  • Invertible contractions and asymptotically stable ODE´s that are not C<sup>1</sup>-linearizable 

    Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2005)
    Article
    Open Access
    We present an example of a contraction di®eomorphism in in¯nite dimensions that is not C1-linearizable, and we construct a regular ordinary di®erential equation in a Hilbert space whose time-one map is that di®eomorphism. ...
  • Known results and open problems on C1 linearization in Banach spaces 

    Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2012)
    Article
    Open Access
    The purpose of this paper is to review the results obtained by the authors on linearization of dynamical systems in infinite dimen- sional Banach spaces, especially in the C 1 case, and also to present some open ...
  • Linearization of class C1 for contractions on Banach Spaces 

    Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2003)
    External research report
    Open Access
    In this work we prove a C1-linearization result for contraction diffeomorphisms, near a fixed point, valid in infinite dimensional Banach spaces. As an intermediate step, we prove a specific result of existence of invariant ...
  • Smooth linearization for a saddle on Banach spaces 

    Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de (2003)
    Article
    Open Access
    As a continuation of a previous work on linearization of class C1 of diffeomorphisms and flows in infinite dimensions near a fixed point, in this work we deal with the case of a saddle point with some non-resonance restrictions ...