D'abord, on étudie trois façons d'associer une C*-algèbre à une transformation continue. Ensuite, nous donnons une nouvelle définition de l'entropie. Nous trouvons des relations entre les états KMS des algèbres préalablement définies et les états d'équilibre, donné par un principe variationnel. Dans la seconde partie, nous étudions les algèbres de Kajiwara-Watatani associees a un système des fonctions itérées. Nous comparons ces algèbres avec l'algèbre de Cuntz et le produit croisé. Enfin, nous étudions les états KMS des algèbres de Kajiwara-Watatani pour les actions provenant d'un potentiel et nous trouvouns des relations entre ces états et les mesures trouvee dans une version de le théorème de Ruelle-Perron-Frobenius pour les systèmes de fonctions itérées. / Primeiramente, estudamos três formas de associar uma C*-álgebra a uma transformação contínua. Em seguida, damos uma nova definição de entropia. Relacionamos, então, os estados KMS das álgebras anteriormente definidas com os estados de equilibro, vindos de um princípio variacional. Na segunda parte, estudamos as álgebras de Kajiwara-Watatani associadas a um sistema de funções iteradas. Comparamos tais álgebras com a álgebra de Cuntz e a álgebra do produto cruzado. Finalmente, estudamos os estados KMS das álgebras de Kajiwara-Watatani para ações vindas de um potencial e relacionamos tais estados KMS com medidas encontradas numa versão do teorema de Ruelle-Perron-Frobenius para sistemas de funções iteradas. / First, we study three ways of associating a C*-algebra to a continuous map. Then, we give a new de nition of entropy. We relate the KMS states of the previously de ned algebras with the equilibrium states, given by a variational principle. In the second part, we study the Kajiwara-Watatani algebras associated to iterated function system. We compare these algebras with the Cuntz algebra and the crossed product. Finally, we study the KMS states of the Kajiwara-Watatani algebras for actions coming from a potential and we relate such states with measures found in a version of the Ruelle-Perron- Frobenius theorem for iterated function systems.

D'abord, on étudie trois façons d'associer une C*-algèbre à une transformation continue. Ensuite, nous donnons une nouvelle définition de l'entropie. Nous trouvons des relations entre les états KMS des algèbres préalablement définies et les états d'équilibre, donné par un principe variationnel. Dans la seconde partie, nous étudions les algèbres de Kajiwara-Watatani associees a un système des fonctions itérées. Nous comparons ces algèbres avec l'algèbre de Cuntz et le produit croisé. Enfin, nous étudions les états KMS des algèbres de Kajiwara-Watatani pour les actions provenant d'un potentiel et nous trouvouns des relations entre ces états et les mesures trouvee dans une version de le théorème de Ruelle-Perron-Frobenius pour les systèmes de fonctions itérées. / Primeiramente, estudamos três formas de associar uma C*-álgebra a uma transformação contínua. Em seguida, damos uma nova definição de entropia. Relacionamos, então, os estados KMS das álgebras anteriormente definidas com os estados de equilibro, vindos de um princípio variacional. Na segunda parte, estudamos as álgebras de Kajiwara-Watatani associadas a um sistema de funções iteradas. Comparamos tais álgebras com a álgebra de Cuntz e a álgebra do produto cruzado. Finalmente, estudamos os estados KMS das álgebras de Kajiwara-Watatani para ações vindas de um potencial e relacionamos tais estados KMS com medidas encontradas numa versão do teorema de Ruelle-Perron-Frobenius para sistemas de funções iteradas. / First, we study three ways of associating a C*-algebra to a continuous map. Then, we give a new de nition of entropy. We relate the KMS states of the previously de ned algebras with the equilibrium states, given by a variational principle. In the second part, we study the Kajiwara-Watatani algebras associated to iterated function system. We compare these algebras with the Cuntz algebra and the crossed product. Finally, we study the KMS states of the Kajiwara-Watatani algebras for actions coming from a potential and we relate such states with measures found in a version of the Ruelle-Perron- Frobenius theorem for iterated function systems.

D'abord, on étudie trois façons d'associer une C*-algèbre à une transformation continue. Ensuite, nous donnons une nouvelle définition de l'entropie. Nous trouvons des relations entre les états KMS des algèbres préalablement définies et les états d'équilibre, donné par un principe variationnel. Dans la seconde partie, nous étudions les algèbres de Kajiwara-Watatani associees a un système des fonctions itérées. Nous comparons ces algèbres avec l'algèbre de Cuntz et le produit croisé. Enfin, nous étudions les états KMS des algèbres de Kajiwara-Watatani pour les actions provenant d'un potentiel et nous trouvouns des relations entre ces états et les mesures trouvee dans une version de le théorème de Ruelle-Perron-Frobenius pour les systèmes de fonctions itérées. / Primeiramente, estudamos três formas de associar uma C*-álgebra a uma transformação contínua. Em seguida, damos uma nova definição de entropia. Relacionamos, então, os estados KMS das álgebras anteriormente definidas com os estados de equilibro, vindos de um princípio variacional. Na segunda parte, estudamos as álgebras de Kajiwara-Watatani associadas a um sistema de funções iteradas. Comparamos tais álgebras com a álgebra de Cuntz e a álgebra do produto cruzado. Finalmente, estudamos os estados KMS das álgebras de Kajiwara-Watatani para ações vindas de um potencial e relacionamos tais estados KMS com medidas encontradas numa versão do teorema de Ruelle-Perron-Frobenius para sistemas de funções iteradas. / First, we study three ways of associating a C*-algebra to a continuous map. Then, we give a new de nition of entropy. We relate the KMS states of the previously de ned algebras with the equilibrium states, given by a variational principle. In the second part, we study the Kajiwara-Watatani algebras associated to iterated function system. We compare these algebras with the Cuntz algebra and the crossed product. Finally, we study the KMS states of the Kajiwara-Watatani algebras for actions coming from a potential and we relate such states with measures found in a version of the Ruelle-Perron- Frobenius theorem for iterated function systems.

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ABSTRACT Although Cotton Mather, as the official chronicler of the 1692 Salem witch trials, is infamously associated with those events, and excerpts from his apologia on Salem, Wonders of the Invisible World, are widely anthologized today, no annotated critical edition of the entire work has appeared in print since the nineteenth century. This present edition of Wonders seeks to remedy this lacuna in modern scholarship. In Wonders, Mather applies both his views on witchcraft and on millennialism to events at Salem. This edition to Mather's Wonders presents this seventeenth-century text beside an integrated theory of the initial causes of the Salem witch panic. The juxtaposition of the probable natural causes of Salem's bewitchment with Mather's implausible explanations exposes the disingenuousness of his writing about Salem. My theory of what happened at Salem includes the probability that a group of conspirators led by the Rev. Samuel Parris deliberately orchestrated the "witchcraft" and that a plant, the thorn apple, used in Algonquian initiation rites, caused the initial symptoms of bewitchment (39-189). Furthermore, key spectral evidence used at the Salem witch trials and recorded by Mather in Wonders appears to have been generated by intense nightmares, commonly thought at the time to be witch visitations, resulting from what is today termed sleep paralysis (215-310). This dissertation provides a detailed look at some of the testimony given in the Salem court records and in Wonders of the Invisible World as it relates to the interpretation in folklore of the phenomenology of nightmares associated with sleep paralysis. The third chapter of this dissertation focuses extensively on Mather's text as a disingenuous response to the Salem witch trials (320-456). The final section of chapter three posits a "Scythian" or Eurasian connection between Swedish and Salem witchcraft. Similarities in shamanic practices among respective indigenous populations of Lapland, Eurasia, Asia, and New England, caused the devil's involvement in both the visible and invisible worlds to appear more than theoretical to writers like Jose Acosta, Johannes Scheffer, Nicholas Fuller, Joseph Mede, Anthony Horneck, and Cotton Mather, inducing Mather to include a lengthy abstract of the Swedish account in Wonders (404-449).

ABSTRACT Although Cotton Mather, as the official chronicler of the 1692 Salem witch trials, is infamously associated with those events, and excerpts from his apologia on Salem, Wonders of the Invisible World, are widely anthologized today, no annotated critical edition of the entire work has appeared in print since the nineteenth century. This present edition of Wonders seeks to remedy this lacuna in modern scholarship. In Wonders, Mather applies both his views on witchcraft and on millennialism to events at Salem. This edition to Mather's Wonders presents this seventeenth-century text beside an integrated theory of the initial causes of the Salem witch panic. The juxtaposition of the probable natural causes of Salem's bewitchment with Mather's implausible explanations exposes the disingenuousness of his writing about Salem. My theory of what happened at Salem includes the probability that a group of conspirators led by the Rev. Samuel Parris deliberately orchestrated the "witchcraft" and that a plant, the thorn apple, used in Algonquian initiation rites, caused the initial symptoms of bewitchment (39-189). Furthermore, key spectral evidence used at the Salem witch trials and recorded by Mather in Wonders appears to have been generated by intense nightmares, commonly thought at the time to be witch visitations, resulting from what is today termed sleep paralysis (215-310). This dissertation provides a detailed look at some of the testimony given in the Salem court records and in Wonders of the Invisible World as it relates to the interpretation in folklore of the phenomenology of nightmares associated with sleep paralysis. The third chapter of this dissertation focuses extensively on Mather's text as a disingenuous response to the Salem witch trials (320-456). The final section of chapter three posits a "Scythian" or Eurasian connection between Swedish and Salem witchcraft. Similarities in shamanic practices among respective indigenous populations of Lapland, Eurasia, Asia, and New England, caused the devil's involvement in both the visible and invisible worlds to appear more than theoretical to writers like Jose Acosta, Johannes Scheffer, Nicholas Fuller, Joseph Mede, Anthony Horneck, and Cotton Mather, inducing Mather to include a lengthy abstract of the Swedish account in Wonders (404-449).