Some aspects of shift-like automorphisms of 
                
                  
                
                $$\pmb {\mathbb {C}}^{\varvec{k}}$$
                
                  
                    
                      
                        C
                      
                      
                        k

Bera, Sayani; Verma, Kaushal

doi:10.1007/s12044-018-0388-1

Cited by 2 publications

(1 citation statement)

References 13 publications

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“…They treated indole-2-carbinols 64 with both 3-alkyl-2-vinyl indoles 5 and tetralone-based enamides 39 under chiral phosphoric acid catalysis and obtained pyrrolo[1,2- a ]indoles 65 and 66 , respectively, with excellent yields, complete diastereoselectivity and very high enantiocontrol (Scheme 20 ). 45 46 Control experiments clearly confirmed the involvement of a bifunctional activation mode of the two components through the chiral phosphoric acid catalyst. Subsequently, the Shi group reported a very similar approach by dimerizing 3-alkyl-2-vinyl indoles under phosphoric acid catalysis to furnish pyrrolo[1,2- a ] indoles via the intermediate indolyl-2-methides.…”

Section: Cycloadditions Of Indolyl-2-methidesmentioning

confidence: 82%

Asymmetric Brønsted Acid Catalyzed Cycloadditions of ortho-Quinone Methides and Related Compounds

Dorsch

Schneider

2022

Synthesis

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This review summarizes recent developments in the area of Brønsted acid-catalyzed, enantioselective cycloadditions of ortho-quinone methides, ortho-quinone methide imines as well as heterocyclic indole- and pyrrol-based methides. In a straightforward and single-step transformation complex polycyclic N- and O-heterocyclic scaffolds are accessible with typically good yields and excellent stereocontrol from simple benzyl and heterobenzyl alcohols upon acid-catalyzed dehydration. The transient precursors are hydrogen-bonded to a chiral Brønsted acid which controls the enantioselectivity of the process.

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Section: Cycloadditions Of Indolyl-2-methidesmentioning

confidence: 82%

Asymmetric Brønsted Acid Catalyzed Cycloadditions of ortho-Quinone Methides and Related Compounds

Dorsch

Schneider

2022

Synthesis

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Dynamical degrees of affine-triangular automorphisms of affine spaces

Blanc¹,

Santen²

2021

Ergod. Th. Dynam. Sys.

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We study the possible dynamical degrees of automorphisms of the affine space $\mathbb {A}^n$ . In dimension $n=3$ , we determine all dynamical degrees arising from the composition of an affine automorphism with a triangular one. This generalizes the easier case of shift-like automorphisms which can be studied in any dimension. We also prove that each weak Perron number is the dynamical degree of an affine-triangular automorphism of the affine space $\mathbb {A}^n$ for some n, and we give the best possible n for quadratic integers, which is either $3$ or $4$ .

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Some aspects of shift-like automorphisms of $$\pmb {\mathbb {C}}^{\varvec{k}}$$ C k

Cited by 2 publications

References 13 publications

Asymmetric Brønsted Acid Catalyzed Cycloadditions of ortho-Quinone Methides and Related Compounds

Asymmetric Brønsted Acid Catalyzed Cycloadditions of ortho-Quinone Methides and Related Compounds

Dynamical degrees of affine-triangular automorphisms of affine spaces

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