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- W4386636706 abstract "Abstract Let <?CDATA $(Sigma_{M},f)$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:mo stretchy=false>(</mml:mo> <mml:msub> <mml:mi mathvariant=normal>Σ</mml:mi> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>f</mml:mi> <mml:mo stretchy=false>)</mml:mo> </mml:math> be a topologically mixing subshift of finite type and let <?CDATA $mathcal{A}:Sigma_{M}to B^times$?> be a Hölder continuous map where <?CDATA $B^{times}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msup> <mml:mi>B</mml:mi> <mml:mrow> <mml:mo>×</mml:mo> </mml:mrow> </mml:msup> </mml:math> is the set of invertible elements of a Banach ring B . We prove that either all ergodic measures have the same maximal Lyapunov exponent, or the irregular set <?CDATA $textrm{Ir}(mathcal{A})$?> is residual in <?CDATA $Sigma_{M}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mi mathvariant=normal>Σ</mml:mi> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> </mml:msub> </mml:math> and has full upper capacity topological entropy of <?CDATA $Sigma_{M}$?> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML overflow=scroll> <mml:msub> <mml:mi mathvariant=normal>Σ</mml:mi> <mml:mrow> <mml:mi>M</mml:mi> </mml:mrow> </mml:msub> </mml:math> . We also prove for generic fiber-bunched cocycles, similar statements can be strengthened by considering the Bowen topological entropy." @default.
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- W4386636706 date "2023-09-08" @default.
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- W4386636706 title "Lyapunov irregular set of Banach cocycles" @default.
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