# American Institute of Mathematical Sciences

May  2022, 42(5): 2433-2437. doi: 10.3934/dcds.2021196

## Erratum and addendum to "A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies" (Volume 40, Number 4, 2020, 2285-2313)

 Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Tokyo, Japan

Received  June 2021 Revised  September 2021 Published  May 2022 Early access  December 2021

We add a lemma implicitly used in the proof of the forward Ergodic Closing Lemma in the paper "A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies" [Discrete Contin. Dyn. Syst., 40 (2020), 2285-2313].

Citation: Shuhei Hayashi. Erratum and addendum to "A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies" (Volume 40, Number 4, 2020, 2285-2313). Discrete and Continuous Dynamical Systems, 2022, 42 (5) : 2433-2437. doi: 10.3934/dcds.2021196
##### References:
 [1] S. Hayashi, A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies, Discrete Contin. Dyn. Syst., 40 (2020), 2285-2313.  doi: 10.3934/dcds.2020114. [2] V. Pliss, A hypothesis due to Smale, Diff. Eq., 8 (1972), 203-214. [3] C. Pugh and C. Robinson, The $C^1$ Closing Lemma, including Hamiltonians, Ergod Th. & Dynam. Sys., 3 (1983), 261-313.  doi: 10.1017/S0143385700001978.

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##### References:
 [1] S. Hayashi, A forward Ergodic Closing Lemma and the Entropy Conjecture for nonsingular endomorphisms away from tangencies, Discrete Contin. Dyn. Syst., 40 (2020), 2285-2313.  doi: 10.3934/dcds.2020114. [2] V. Pliss, A hypothesis due to Smale, Diff. Eq., 8 (1972), 203-214. [3] C. Pugh and C. Robinson, The $C^1$ Closing Lemma, including Hamiltonians, Ergod Th. & Dynam. Sys., 3 (1983), 261-313.  doi: 10.1017/S0143385700001978.
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