Smooth roughness of exponential dichotomies, revisited | Zendy

Christian Pötzsche | Zendy

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Smooth roughness of exponential dichotomies, revisited

Author(s) -

Christian Pötzsche

Publication year - 2015

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2015.20.853

Subject(s) - dichotomy , differentiable function , exponential dichotomy , exponential function , mathematics , saddle point , saddle , invariant (physics) , mathematical analysis , pure mathematics , geometry , differential equation , mathematical optimization , mathematical physics , statistics

As a direct consequence of well-established proof techniques, we establish that the invariant projectors of exponential dichotomies for parameter-dependent nonautonomous difference equations are as smooth as their right-hand sides. For instance, this guarantees that the saddle-point structure in the vicinity of hyperbolic solutions inherits its differentiability properties from the particular given equation.

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