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Extremes and extremal indices for level set observables on hyperbolic systems*MC and MN were supported in part by NSF Grants DMS 1600780 and DMS 2009923. MH acknowledges support of EPSRC grant: EP/P034489/. MC thanks the Max Planck Institute-PKS, Dresden, for their hospitality while part of this work was completed. We would like to thank R Sturman and J Myers Hill for their careful reading and comments. We also thank the anonymous referees for their detailed and helpful suggestions. (8th February 2021)
Record Type:
Journal Article
Title:
Extremes and extremal indices for level set observables on hyperbolic systems*MC and MN were supported in part by NSF Grants DMS 1600780 and DMS 2009923. MH acknowledges support of EPSRC grant: EP/P034489/. MC thanks the Max Planck Institute-PKS, Dresden, for their hospitality while part of this work was completed. We would like to thank R Sturman and J Myers Hill for their careful reading and comments. We also thank the anonymous referees for their detailed and helpful suggestions. (8th February 2021)
Main Title:
Extremes and extremal indices for level set observables on hyperbolic systems*MC and MN were supported in part by NSF Grants DMS 1600780 and DMS 2009923. MH acknowledges support of EPSRC grant: EP/P034489/. MC thanks the Max Planck Institute-PKS, Dresden, for their hospitality while part of this work was completed. We would like to thank R Sturman and J Myers Hill for their careful reading and comments. We also thank the anonymous referees for their detailed and helpful suggestions.
Abstract: Consider an ergodic measure preserving dynamical system ( T, X, μ ), and an observable ϕ : X → R . For the time series X n ( x ) = ϕ ( T n ( x )), we establish limit laws for the maximum process M n = max k ⩽ n X k in the case where ϕ is an observable maximized on a line segment, and ( T, X, μ ) is a hyperbolic dynamical system. Such observables arise naturally in weather and climate applications. We consider the extreme value laws and extremal indices for these observables on hyperbolic toral automorphisms, Sinai dispersing billiards and coupled expanding maps. In particular we obtain clustering and nontrivial extremal indices due to self intersection of submanifolds under iteration by the dynamics, not arising from any periodicity.