03434nam a22004695i 4500001001800000003000900018005001700027007001500044008004100059020001800100024003500118050001400153072001700167072002300184072001600207100014900223245022500372250001800597264006900615300006300684336002600747337002600773338003600799347002400835490005400859505029000913520100901203650002302212650002302235700007802258700007802336700007702414700007902491700008202570700008002652710003402732773002602766776003602792776003602828830005402864856004602918978-3-031-62014-0DE-He21320251030113121.0cr nn 008mamaa241002s2024    sz |    s    |||| 0|eng d  a97830316201407 a10.1007/978-3-031-62014-02doi 4aQA843-871 7aGPFC2bicssc 7aMAT0340002bisacsh 7aGPFC2thema1 aEinsiedler, Manfred.eauthor.0(orcid)0009-0001-2372-58941https://orcid.org/0009-0001-2372-58944aut4http://id.loc.gov/vocabulary/relators/aut10aModern Aspects of Dynamical Systemsh[electronic resource] :bCetraro, Italy 2021 /cby Manfred Einsiedler, Giovanni Forni, Vadim Kaloshin, Jasmin Raissy ; edited by Claudio Bonanno, Alfonso Sorrentino, Corinna Ulcigrai.  a1st ed. 2024. 1aCham :bSpringer Nature Switzerland :bImprint: Springer,c2024.  aXI, 224 p. 30 illus., 3 illus. in color.bonline resource.  atextbtxt2rdacontent  acomputerbc2rdamedia  aonline resourcebcr2rdacarrier  atext filebPDF2rda1 aC.I.M.E. Foundation Subseries,x2946-1820 ;v23470 a- Homogeneous Dynamics and its connection to Diophantine Approximation -- Effective unique ergodicity and weak mixing of translation flows -- Lecture notes on Birkhoff billiards: dynamics, integrability and spectral rigidity -- Introduction to Fatou components in holomorphic dynamics.  aThis book provides an overview of recent advances in the theory of dynamical systems, with a particular emphasis on their connections to other areas of mathematical research, including number theory, geometry, mathematical physics, complex analysis, and celestial mechanics. Compiling the lecture notes from some of the contributions presented at the C.I.M.E. school "Modern Aspects of Dynamical Systems" held in Cetraro in August 2021, the contributions are the following: “Homogeneous dynamics and Diophantine problems” by Manfred Einsiedler, “Effective ergodic theory for translation flow” by Giovanni Forni, “Integrability and rigidity for convex billiards” by Vadim Kaloshin, “Holomorphic dynamics” by Jasmin Raissy and “Exponentially small phenomena and its role in the dynamics” by Tere Martinez-Seara. These notes are suitable for graduate students and young researchers interested in an introduction to some of the modern research areas within the field of dynamical systems. 0aDynamical systems.14aDynamical Systems.1 aForni, Giovanni.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut1 aKaloshin, Vadim.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut1 aRaissy, Jasmin.eauthor.4aut4http://id.loc.gov/vocabulary/relators/aut1 aBonanno, Claudio.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt1 aSorrentino, Alfonso.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt1 aUlcigrai, Corinna.eeditor.4edt4http://id.loc.gov/vocabulary/relators/edt2 aSpringerLink (Online service)0 tSpringer Nature eBook08iPrinted edition:z978303162013308iPrinted edition:z9783031620157 0aC.I.M.E. Foundation Subseries,x2946-1820 ;v234740uhttps://doi.org/10.1007/978-3-031-62014-0