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020 a| 9781470449582q| (paperback);

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100 1 a| Gignac, William.?| UNAUTHORIZED;

245 10 a| Local dynamics of non-invertible maps near normal surface singularitiesh| [electronic resource] /c| William Gignac, Matteo Ruggiero.;

260 a| Providence, RI :b| AMS, American Mathematical Society,c| 2021.;

300 a| xi, 100 pages :b| illustrations ;c| 26 cm;

490 0 a| Memoirs of the American Mathematical Society,x| 0065-9266 ;v| volume 272, number 1337 (July 2021);

504 a| Includes bibliographical references.;

505 0 a| Normal surface singularities, resolutions, and intersection theory -- Normal surface singularities and their valuation spaces -- Log discrepancy, essential skeleta, and special singularities -- Dynamics on valuation spaces -- Dynamics of non-finite germs -- Dynamics of non-invertible finite germs -- Algebraic stability -- Attraction rates -- Examples and remarks.;

506 a| Available only to authorized users.;

520 a| "We study the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs f : (X, x0) (X, x0), where X is a complex surface having x0 as a normal singularity. We prove that as long as x0 is not a cusp singularity of X, then it is possible to find arbitrarily high modifications : X (X, x0) such that the dynamics of f (or more precisely of f N for N big enough) on X is algebraically stable. This result is proved by understanding the dynamics induced by f on a space of valuations associated to X; in fact, we are able to give a strong classification of all the possible dynamical behaviors of f on this valuation space. We also deduce a precise description of the behavior of the sequence of attraction rates for the iterates of f . Finally, we prove that in this setting the first dynamical degree is always a quadratic integer"--c| Provided by publisher.;

538 a| Mode of access: World Wide Web;

650 0 a| Singularities (Mathematics)=| ^A62881;

650 0 a| Holomorphic mappings.=| ^A72214;

650 0 a| Germs (Mathematics)=| ^A77200;

650 0 a| Holomorphic functions.=| ^A58602;

650 7 a| Several complex variables and analytic spaces -- Singularities -- Local singularities.2| msc;

650 7 a| Several complex variables and analytic spaces -- Holomorphic mappings and correspondences -- Iteration problems.2| msc;

650 7 a| Commutative algebra -- General commutative ring theory -- Valuations and their generalizations.2| msc;

650 7 a| Dynamical systems and ergodic theory -- Arithmetic and non-Archimedean dynamical systems -- Dynamical systems on Berkovich spaces.2| msc;

650 7 a| Several complex variables and analytic spaces -- Singularities -- Modifications; resolution of singularities.2| msc;

655 0 a| Electronic books.=| ^A491897;

700 1 a| Ruggiero, Matteo Luca.?| UNAUTHORIZED;

856 40 z| Full text available from Ebook Central - Academic Completeu| https://ebookcentral.proquest.com/lib/eastcarolina/detail.action?docID=6798074;

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Local dynamics of non-invertible maps near normal surface singularities / William Gignac, Matteo Ruggiero.

Author/creator	Gignac, William
Other author	Ruggiero, Matteo Luca.
Format	Electronic
Publication Info	Providence, RI : AMS, American Mathematical Society, 2021.
Description	xi, 100 pages : illustrations ; 26 cm
Supplemental Content	Full text available from Ebook Central - Academic Complete
Subjects	Singularities (Mathematics) Holomorphic mappings. Germs (Mathematics) Holomorphic functions.

Series	Memoirs of the American Mathematical Society, 0065-9266 ; volume 272, number 1337 (July 2021)
Contents	Normal surface singularities, resolutions, and intersection theory -- Normal surface singularities and their valuation spaces -- Log discrepancy, essential skeleta, and special singularities -- Dynamics on valuation spaces -- Dynamics of non-finite germs -- Dynamics of non-invertible finite germs -- Algebraic stability -- Attraction rates -- Examples and remarks.
Abstract	"We study the problem of finding algebraically stable models for non-invertible holomorphic fixed point germs f : (X, x0) (X, x0), where X is a complex surface having x0 as a normal singularity. We prove that as long as x0 is not a cusp singularity of X, then it is possible to find arbitrarily high modifications : X (X, x0) such that the dynamics of f (or more precisely of f N for N big enough) on X is algebraically stable. This result is proved by understanding the dynamics induced by f on a space of valuations associated to X; in fact, we are able to give a strong classification of all the possible dynamical behaviors of f on this valuation space. We also deduce a precise description of the behavior of the sequence of attraction rates for the iterates of f . Finally, we prove that in this setting the first dynamical degree is always a quadratic integer"-- Provided by publisher.
Bibliography note	Includes bibliographical references.
Access restriction	Available only to authorized users.
Technical details	Mode of access: World Wide Web
Genre/form	Electronic books.
LCCN	2022007634
ISBN	9781470449582 (paperback)
ISBN	(epub)

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Local dynamics of non-invertible maps near normal surface singularities / William Gignac, Matteo Ruggiero.

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