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arXiv · 2401.13367

Invariant measures from locally bounded orbits

Antoni López-Martínez
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Abstract

Motivated by recent investigations of Sophie Grivaux and \'Etienne Matheron on the existence of invariant measures in Linear Dynamics, we introduce the concept of locally bounded orbit for a continuous linear operator $T:X\longrightarrow X$ acting on a Fr\'echet space $X$, and we use this new notion to construct (non-trivial) $T$-invariant probability Borel measures on $(X,\mathscr{B}(X))$.

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Antoni López-Martínez. 2024-01-24. Invariant measures from locally bounded orbits. https://doi.org/10.1007/s00025-024-02204-5

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