We study actions of finitely generated groups on $\bbR$-trees under somestability hypotheses. We prove that either the group splits over somecontrolled subgroup (fixing an arc in particular), or the action can beobtained by gluing together actions of simple types: actions on simplicialtrees, actions on lines, and actions coming from measured foliations on2-orbifolds. This extends results by Sela and Rips-Sela. However, their resultsare misstated, and we give a counterexample to their statements. The proof relies on an extended version of Scott's Lemma of independentinterest. This statement claims that if a group $G$ is a direct limit of groupshaving suitably compatible splittings, then $G$ splits.
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机译：我们在稳定性假设下研究$ \ bbR $树上有限生成群的行为。我们证明，该组要么分裂成某个受控子组（特别是固定弧），要么可以通过将简单类型的动作粘合在一起来获得该动作：简单树上的动作，直线上的动作以及来自测得的叶面在2维上的动作。这扩展了Sela和Rips-Sela的结果。但是，他们的结果是错误的，我们为他们的陈述提供了反例。该证明依赖于Scott的独立利益引理的扩展版本。该声明声称，如果组$ G $是具有适当兼容拆分的组的直接限制，则$ G $拆分。
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